Surveillance Using Particulate Tracers

ABSTRACT

In accordance with some embodiments, a method of determining a flow profile for a wellbore using unique particulate tracers is disclosed. At least one unique particulate tracer is pumped throughout each stage, each stage group, or any combination thereof during a hydraulic fracturing operation performed in the subterranean formation

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 63/288,447 titled “Surveillance Using Particulate Tracers” andfiled on Dec. 10, 2021, the entire contents of which are herebyincorporated by reference. This application is related to two otherco-pending applications, filed on even date herewith, and identified byAttorney Docket number T-11543A-US01, title: “Surveillance UsingParticulate Tracers”, and publication number ______ and Attorney Docketnumber T-11543B-US01, title: “Surveillance Using Particulate Tracers”,and publication number ______, all of which are incorporated byreference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

TECHNICAL FIELD

The disclosed embodiments relate generally to techniques forsurveillance using particulate tracers.

BACKGROUND

Tracers are used in the hydrocarbon industry to track flow patterns andrates of the particular fluid to which it is introduced. Tracers arealso used to study properties of the subterranean formation in which thefluid resides. Tracers commonly are chemical compounds that havenegligible effects on the fluid. In operation, tracers are injected intothe subterranean formation, and thereafter produced and sampled tomeasure for tracer concentration. There exists a need for surveillanceusing particulate tracers.

SUMMARY

In accordance with some embodiments, a method of determining a flowprofile for a wellbore using unique particulate tracers is disclosed.The method comprises obtaining produced fluid samples comprising uniqueparticulate tracers from a wellbore drilled into a subterraneanformation, wherein at least one unique particulate tracer is pumpedthroughout each stage, each stage group, or any combination thereofduring a hydraulic fracturing operation performed in the subterraneanformation, and wherein each unique particulate tracer corresponds to anoil phase, a water phase, or a gas phase, and wherein the produced fluidsamples comprise at least a portion of the unique particulate tracersthat were pumped throughout the stages, the stage groups, or anycombination thereof. The method further comprises determining a flowprofile for the wellbore for each phase using the produced fluid samplescomprising the unique particulate tracers by: a) obtaining a tracerconcentration history for each unique particulate tracer; b) obtaining aproduction history for the wellbore; c) determining a mean residencetime for each unique particulate tracer using the corresponding tracerconcentration history; d) determining a contact volume proxy for eachunique particulate tracer using the production history and thecorresponding tracer concentration history; and e) determining the flowprofile for the wellbore for each phase indicative of flow contributionof each stage, each stage group, or any combination thereof by using thecorresponding mean residence times and the corresponding contact volumeproxies.

In accordance with some embodiments, a method of determining a flowprofile for a wellbore using unique particulate tracers, the methodbeing implemented in a computer system that includes a physical computerprocessor and non-transitory storage medium. The method comprises: a)obtaining, from a non-transitory storage medium, a tracer concentrationhistory for each unique particulate tracer in produced fluid samplesfrom a wellbore drilled into a subterranean formation, wherein at leastone unique particulate tracer is pumped throughout each stage, eachstage group, or any combination thereof during a hydraulic fracturingoperation performed in the subterranean formation, and wherein eachunique particulate tracer corresponds to an oil phase, a water phase, ora gas phase, and wherein the produced fluid samples comprise at least aportion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof. The methodfurther comprises b) obtaining, from the non-transitory storage medium,a production history for the wellbore; c) determining, with a physicalcomputer processor, a mean residence time for each unique particulatetracer using the corresponding tracer concentration history; d)determining, with the physical computer processor, a contact volumeproxy for each unique particulate tracer using the production historyand the corresponding tracer concentration history; and e) determining,with the physical computer processor, a flow profile for the wellborefor each phase indicative of flow contribution of each stage, each stagegroup, or any combination thereof by using the corresponding meanresidence times and the corresponding contact volume proxies.

In accordance with some embodiments, a method of determining a flowprofile for a wellbore using unique particulate tracers. The methodcomprises obtaining produced fluid samples comprising unique particulatetracers from a wellbore drilled into a subterranean formation, whereinat least one unique particulate tracer is pumped throughout each stage,each stage group, or any combination thereof during a hydraulicfracturing operation performed in the subterranean formation, andwherein each unique particulate tracer corresponds to an oil phase, awater phase, or a gas phase, and wherein the produced fluid samplescomprise at least a portion of the unique particulate tracers that werepumped throughout the stages, the stage groups, or any combinationthereof. The method further comprises determining a flow profile for thewellbore for each phase using the produced fluid samples comprising theunique particulate tracers by: a) obtaining a tracer concentrationhistory for each unique particulate tracer; b) optionally obtaining aproduction history for the wellbore; c) determining a decline rate foreach unique particulate tracer using the corresponding tracerconcentration history; d) determining a normalization factor for eachunique particulate tracer using the corresponding tracer concentrationhistory and optionally the production history; e) determining anormalized decline rate for each unique particulate tracer using thecorresponding decline rate and the corresponding normalization factor;and f) determining a flow profile for the wellbore for each phaseindicative of flow contribution of each stage, each stage group, or anycombination thereof by using the corresponding normalized decline rates.

In accordance with some embodiments, a method of determining a flowprofile for a wellbore using unique particulate tracers, the methodbeing implemented in a computer system that includes a physical computerprocessor and non-transitory storage medium. The method comprises a)obtaining, from the non-transitory storage medium, a tracerconcentration history for each unique particulate tracer in producedfluid samples from a wellbore drilled into a subterranean formation,wherein at least one unique particulate tracer is pumped throughout eachstage, each stage group, or any combination thereof during a hydraulicfracturing operation performed in the subterranean formation, andwherein each unique particulate tracer corresponds to an oil phase, awater phase, or a gas phase, and wherein the produced fluid samplescomprise at least a portion of the unique particulate tracers that werepumped throughout the stages, the stage groups, or any combinationthereof. The method further comprises b) optionally obtaining, from thenon-transitory storage medium, a production history for the wellbore; c)determining, with the physical computer processor, a decline rate foreach unique particulate tracer using the corresponding tracerconcentration history; d) determining, with the physical computerprocessor, a normalization factor for each unique particulate tracerusing the corresponding tracer concentration history and optionally theproduction history; e) determining, with the physical computerprocessor, a normalized decline rate for each unique particulate tracerusing the corresponding decline rate and the corresponding normalizationfactor; and f) determining, with the physical computer processor, a flowprofile for the wellbore for each phase indicative of flow contributionof each stage, each stage group, or any combination thereof by using thecorresponding normalized decline rates.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A, 1B, and 1C show a field system, and details thereof, withwhich example embodiments can be used.

FIGS. 1D-1, 1D-2, 1D-3 illustrates examples of unique particulatetracers pumped throughout stages in the context of a single wellbore.

FIGS. 1E-1, 1E-2, 1E-3 illustrates examples of unique particulatetracers pumped throughout stages in the context of multiple wellbores.

FIG. 1F illustrates that the unique particulate tracers may react anddiffuse into flowing fluid and the fluid may be produced from a wellboreas produced fluid.

FIG. 1G-1H illustrate diagram related to binary response.

FIG. 2A-2D illustrate embodiments of pumping unique particulate tracersin the near wellbore region in the context of a single wellbore.

FIG. 3A-3C illustrate embodiments of pumping unique particulate tracersin the near wellbore region in the context of a multiple wellbores.

FIG. 4 illustrates an example method of placing unique particulatetracers in a subterranean formation having a wellbore therewithin.

FIG. 5 illustrates an example of V_(wellbore,min) and L_(wellbore,min).

FIG. 6 illustrates an expected tracer release rate plot.

FIG. 7A-7G include various examples consistent with the disclosure.

FIG. 8 illustrates an example computer system consistent with thedisclosure.

FIG. 9 illustrates an example method of determining a flow profile for awellbore using unique particulate tracers

FIG. 10 illustrates more information including the Δt, which is arrivaltime difference.

FIG. 11-22 illustrate various ways to refine the wellbore volume andvarious other optional steps.

FIG. 23 illustrates an example computer system consistent with thedisclosure.

FIG. 24 illustrates an example computer system consistent with thedisclosure.

FIG. 25 illustrates an example method for determining a flow profile fora wellbore using unique particulate tracers.

FIG. 26A illustrates one diagram regarding mean residence time. FIG. 26Billustrates one diagram regarding contact volume proxy.

FIG. 27 illustrates an example method for determining a flow profile fora wellbore using unique particulate tracers.

FIG. 28A-28B illustrate an example of shut-in to build up tracer clouds.

FIG. 29 illustrates an example computer system consistent with thedisclosure.

FIG. 30 illustrates an example method for determining a flow profile fora wellbore using unique particulate tracers.

FIG. 31A-31B illustrate two diagrams regarding decline rate.

FIG. 32 illustrates an example method for determining a flow profile fora wellbore using unique particulate tracers.

FIG. 33A-33H illustrate various examples of flow profiles for an oilphase only and corresponding tracer concentrations histories for theexamples.

FIGS. 34A-34B and 35A also illustrate tracer concentration historiesused with the response time delay method and the decline method as inFIGS. 34C and 35B, respectively.

FIG. 36 illustrates an example computer system consistent with thedisclosure.

Various embodiments and examples are provided in the various figures.Like reference numerals refer to corresponding parts throughout thedrawings.

DETAILED DESCRIPTION OF EMBODIMENTS

PARTICULATE TRACERS: The term “particulate tracers” is utilized hereinto refer to solid particles with chemical tracers bound to them. Theparticulate tracers may be practically any particulate tracers known inthe art, such as particulate tracers for hydrocarbons (e.g., oil),particulate tracers for water, particulate tracers for gas, or anycombination thereof. For example, types of particulate tracers that areintroduced into the subterranean formation may include, but are notlimited to, fluorinated benzoic acids (FBAs), fluorescein dyes,FBA/fluorescein synthesis, fluorescing nanocrystals, radioactivetracers, fluorescing nanoparticles, magnetic nanoparticle tracers, etc.

Particulate tracers may differ in density, for example, from specificgravity of 0.90 to 2.75 (e.g., 0.96 to 2.65 in one embodiment, 0.96 to1.5 in a second embodiment, etc.). The density may affect rheology andflow. The average size of particulate tracer particles may be 40 mesh to100 mesh. Particulate tracers generally release at the same rateindependent of the flowrate. The particulate tracers may besubstantially the same size as proppant particles, and as such, theparticulate tracers may be pumped with proppant particles and stay withthe proppant particles (sometimes simply referred to as “proppant”).Those of ordinary skill in the art will appreciate that the term“particulate tracer” is not meant to be limited, and the term“particulate tracer” may include practically any substance that canfunction as a particulate tracer as discussed herein.

For simplicity, the term “unique particulate tracer” is utilized hereinto distinguish between different particulate tracers. A uniqueparticulate tracer includes at least one solid particle comprisingtracer material. To further distinguish different unique particulatetracers, sometimes the term first, second, each, etc. may be utilizedherein (e.g., first unique oil particulate tracer, second unique oilparticulate tracer, each unique oil particulate tracer, etc.).Furthermore, a specific particulate tracer, such as a first unique oilparticulate tracer, may be pumped into a single stage or a stage groupthat comprises at least two stages due to a shortage of differentparticulate tracers, costs, logistics, or other reasons. For simplicity,those of ordinary skill in the art will appreciate that discussion of a“stage” may also include a “stage group” herein unless stated otherwise.

In the existing practice, a unique oil particulate tracer may be pumpedthroughout each stage and/or stage group if there is an interest in oil.A unique water particulate tracer may be pumped throughout each stageand/or stage group if there is an interest in water. A unique gasparticulate tracer may be pumped throughout each stage and/or stagegroup if there is an interest in gas. FIGS. 1D-1, 1D-2, 1D-3, 1E-1,1E-2, and 1E-3 illustrate different pumping options in which uniqueparticulate tracers are pumped throughout stages and/or stage groups.

As illustrated in FIG. 1F, the unique particulate tracers may react anddiffuse into flowing fluid and the fluid may be produced from a wellboreas produced fluid. For example, unique oil particulate tracers may reactand diffuse into the fluid in response to contact with oil in the fluid.Similarly, unique water particulate tracers may react and diffuse intothe fluid in response to contact with water in the fluid. Similarly,unique gas particulate tracers may react and diffuse into the fluid inresponse to contact with gas in the fluid. Similarly, in a single stageof a hydraulic fracturing operation, different particulate tracers mayreact and diffuse into the fluid in response to contact with thecorresponding item in the fluid. For example, in a single stage of ahydraulic fracturing operation, a unique oil particulate tracer maydiffuse into the fluid in response to contact with oil in the fluid anda unique gas particulate tracer may diffuse into the fluid in responseto contact with gas in the fluid. The produced fluid may be sampled toanalyze the unique particulate tracers in the samples. Each uniqueparticulate tracer pumped into a stage and/or stage group may depend onthe desired information that is sought about that stage and/or stagegroup as discussed further hereinbelow.

Placing Unique Particulate Tracers in a Subterranean Formation Having aWellbore Therewithin Such that a Substantial Portion of the UniqueParticulate Tracers are Placed in a Near Wellbore Region of theSubsurface Formation Proximate to the Wellbore:

Described below are methods and systems of placing unique particulatetracers in a subterranean formation having a wellbore therewithin. Theseembodiments are designed to be of particular use for surveillance withina subsurface formation, including generating flow rates (e.g., barrelsper day). The embodiments described herein place particulate tracers inat least two stages, including a first stage and a second stage, duringa hydraulic fracturing operation in the subsurface formation. Theparticulate tracers are pumped only in a fraction of each stage and/oreach stage group such that a substantial portion of the uniqueparticulate tracers are placed in a near wellbore region of thesubsurface formation proximate to the wellbore. As will be describedfurther, the embodiments provided herein improve upon existingapproaches to placing unique particulate tracers in a subterraneanformation.

Reference will now be made in detail to various embodiments, examples ofwhich are illustrated in the accompanying drawings. In the followingdetailed description, numerous specific details are set forth in orderto provide a thorough understanding of the present disclosure and theembodiments described herein. However, embodiments described herein maybe practiced without these specific details. In other instances,well-known methods, procedures, components, and mechanical apparatushave not been described in detail so as not to unnecessarily obscureaspects of the embodiments.

Example embodiments of placing unique particular tracers in a subsurfaceformation having a wellbore therewithin will be described more fullyhereinafter with reference to the accompanying drawings. Placing uniqueparticular tracers in a subterranean formation having a wellboretherewithin may, however, be embodied in many different forms and shouldnot be construed as limited to the example embodiments set forth herein.Rather, these embodiments and examples are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of placing unique particular tracers in a subterranean formationhaving a wellbore therewithin to those of ordinary skill in the art.Like, but not necessarily the same, elements (also sometimes calledcomponents) in the various figures are denoted by like referencenumerals for consistency.

FIGS. 1A through 1C show a field system 199, including details thereof,with which example embodiments can be used. Specifically, FIG. 1A showsa schematic diagram of a land-based field system 199 in which a wellbore120 has been drilled in a subterranean formation 110. FIG. 1B shows adetail of a substantially horizontal section 103 of the wellbore 120 ofFIG. 1A. FIG. 1C shows a detail of an induced fracture 101 of FIG. 1B.The field system 199 in this example includes a wellbore 120 disposed ina subterranean formation 110 using field equipment 109 (e.g., a derrick,a tool pusher, a clamp, a tong, drill pipe, casing pipe, a drill bit, awireline tool, a fluid pumping system) located above a surface 108 andwithin the wellbore 120. Once the wellbore 120 is drilled, a casingstring 125 is inserted into the wellbore 120 to stabilize the wellbore120 and allow for the extraction of subterranean resources (e.g.,hydrocarbon such as natural gas, oil) from the subterranean formation110.

The surface 108 can be ground level for an onshore application and thesea floor/lakebed for an offshore application. For offshoreapplications, at least some of the field equipment can be located on aplatform that sits above the water level. The point where the wellbore120 begins at the surface 108 can be called the wellhead. While notshown in FIGS. 1A and 1B, there can be multiple wellbores 120, each withits own wellhead but that is located close to the other wellheads,drilled into the subterranean formation 110 and having substantiallyhorizontal sections 103 that are close to each other. In such a case,the multiple wellbores 120 can be drilled at the same pad or atdifferent pads. When the drilling process is complete, other operations,such as fracturing operations, can be performed. The fractures 101 areshown to be located in the horizontal section 103 of the wellbore 120 inFIG. 1B. The fractures 101, whether induced and/or naturally occurring,can additionally or alternatively be located in other sections (e.g., asubstantially vertical section, a transition area between a verticalsection and a horizontal section) of the wellbore 120. Exampleembodiments can be used along any portion of the wellbore 120 wherefractures 101 are located.

The subterranean formation 110 can include one or more of a number offormation types, including but not limited to shale, limestone,sandstone, clay, sand, and salt. In certain embodiments, a subterraneanformation 110 can include one or more reservoirs in which one or moreresources (e.g., oil, natural gas, water, steam) can be located. One ormore of a number of field operations (e.g., fracturing, coring,tripping, drilling, setting casing, extracting downhole resources) canbe performed to reach an objective of a user with respect to thesubterranean formation 110.

The wellbore 120 can have one or more of a number of segments or holesections, where each segment or hole section can have one or more of anumber of dimensions. Examples of such dimensions can include, but arenot limited to, a size (e.g., diameter) of the wellbore 120, a curvatureof the wellbore 120, a total vertical depth of the wellbore 120, ameasured depth of the wellbore 120, and a horizontal displacement of thewellbore 120. There can be multiple overlapping casing strings ofvarious sizes (e.g., length, outer diameter) contained within andbetween these segments or hole sections to ensure the integrity of thewellbore construction. In this case, one or more of the segments of thesubterranean wellbore 120 is the substantially horizontal section 103.As stated above, in additional or alternative cases, one or more of thesegments of the subterranean wellbore 120 is a substantially verticalsection.

As discussed above, inserted into and disposed within the wellbore 120of FIGS. 1A and 1B are a number of casing pipes that are coupled to eachother end-to-end to form the casing string 125. In this case, each endof a casing pipe has mating threads (a type of coupling feature)disposed thereon, allowing a casing pipe to be directly or indirectlymechanically coupled to another casing pipe in an end-to-endconfiguration. The casing pipes of the casing string 125 can beindirectly mechanically coupled to each other using a coupling device,such as a coupling sleeve.

Each casing pipe of the casing string 125 can have a length and a width(e.g., outer diameter). The length of a casing pipe can vary. Forexample, a common length of a casing pipe is approximately 40 feet. Thelength of a casing pipe can be longer (e.g., 60 feet) or shorter (e.g.,10 feet) than 40 feet. The width of a casing pipe can also vary and candepend on the cross-sectional shape of the casing pipe. For example,when the shape of the casing pipe is cylindrical, the width can refer toan outer diameter, an inner diameter, or some other form of measurementof the casing pipe. Examples of a width in terms of an outer diametercan include, but are not limited to, 4½ inches, 7 inches, 7⅝ inches, 8⅝inches, 10¾ inches, 13⅜ inches, and 14 inches.

The size (e.g., width, length) of the casing string 125 can be based onthe information (e.g., diameter of the borehole drilled) gathered usingfield equipment with respect to the subterranean wellbore 120. The wallsof the casing string 125 have an inner surface that forms a cavity 165that traverses the length of the casing string 125. Each casing pipe canbe made of one or more of a number of suitable materials, including butnot limited to steel. Cement 109 is poured into the wellbore 120 throughthe cavity 165 and then forced upward between the outer surface of thecasing string 125 and the wall of the subterranean wellbore 120. In somecases, a liner may additionally be used with, or alternatively be usedin place of, some or all of the casing pipes.

Once the cement dries to form concrete, a number of fractures 101 areinduced in the subterranean formation 110. The fractures 101 can beinduced by hydraulic fracturing. The hydraulic fracturing processinvolves the injection of large quantities of fluids containing water,chemical additives, and proppant 112 into the subterranean formation 110from the wellbore 120 to create fracture networks. A subterraneanformation 110 naturally has fractures 101, but these naturally occurringfractures 101 have inconsistent characteristics (e.g., length, spacing)and so in some cases cannot be relied upon for extracting subterraneanresources without having additional fractures 101, such as what is shownin FIG. 1B, induced in the subterranean formation 110.

Operations that induce fractures 101 in the subterranean formation 110use any of a number of fluids that include proppant 112 (e.g., sandparticles, ceramic pellets). When proppant 112 is used, some of thefractures 101 (also sometimes called principal or primary fractures)receive proppant 112, while a remainder of the fractures 101 (alsosometimes called secondary fractures) do not have any proppant 112 inthem.

As shown in FIG. 1C, the proppant 112 is designed to become lodgedinside at least some of the induced fractures 101 to keep thosefractures 101 open after the fracturing operation is complete. The sizeof the proppant 112 is an important design consideration. Sizes (e.g.,40/70 mesh, 50/140 mesh) of the proppant 112 can vary. While the shapeof the proppant 112 is shown as being uniformly spherical, and the sizeis substantially identical among the proppant 112, the actual sizes andshapes of the proppant 112 can vary. If the proppant 112 is too small,the proppant 112 will not be effective at keeping the fractures 101 openenough to effectively allow subterranean resources 111 to flow throughthe fractures 101 from the rock matrices 162 in the subterraneanformation 110 to the wellbore 120. If the proppant 112 is too large, theproppant 112 can plug up the fractures 101, blocking the flow of thesubterranean resources 111 through the fractures 101.

The use of proppant 112 in certain types of subterranean formation 110,such as shale, is important. Shale formations typically havepermeabilities on the order of microdarcys (mD) to nanodarcys (nD). Whenfractures 101 are induced in such formations with low permeabilities, itis important to sustain the fractures 101 and their conductivity for anextended period of time in order to extract more of the subterraneanresource 111.

The wellbore 120 is hydraulically fractured in terms of stages, whichare illustrated as Stage1 to StageN in FIGS. 1D-1, 1D-2, 1D-3, 1E-1,1E-2, and 1E-3 . Each stage includes single or multiple perforationsclusters and the fractures 101 are induced from the perforationclusters. Additionally, unique particulate tracers are pumped with theproppant 112 for surveillance purposes to track flow patterns and ratesof the fluid to which it is introduced.

In existing practice, a unique particulate tracer is typically pumpedthroughout each stage to determine over time which stage is contributingto water or hydrocarbon (e.g., oil) flow. The unique particulate tracersare chemical compounds that have negligible effects on the fluidcarrying the particulate tracers. In the existing practice, the uniqueparticulate tracers are pumped throughout the stages and/or throughoutthe stage groups with the proppant such as illustrated in FIGS. 1D-1,1D-2, 1D-3, 1E-1, 1E-2, and 1E-3 , and thereafter, at least a portionthe unique particulate tracers are produced in the produced fluid andsampled to measure for tracer concentration. A field operator manuallycollects at least one sample from the produced fluid, transports the atleast one sample to a laboratory, filters the at least one sample, andfinally analyzes the at least one sample for tracer concentration. Theexisting practice of pumping unique particulate tracers 170 (illustratedas 170 a _(oil), 170 b _(oil), and so on) with the proppant 112 in theentirety of each Stage1 through StageN for a single wellbore 120 isillustrated in as illustrated FIGS. 1D-1, 1D-2, 1D-3, 1E-1, 1E-2, and1E-3 . The existing practice of pumping unique particulate tracers 170with the proppant 112 in the entirety of each Stage1 through StageN fora plurality of wellbores, such as the wellbore 120 and two offsethorizontal wellbores 175, is illustrated in FIGS. 1E-1, 1E-2, and 1E-3 .Due to the limited quantity of unique particulate tracers, costs,logistics, etc., a unique particulate tracer may be pumped with theproppant in the entirety of each stage and/or stage group (i.e., aplurality of stages) in the existing practice.

The existing practice, as illustrated in FIG. 1D-1, 1D-2, 1D-3, 1E-1,1E-2, 1E-3 , requires a large quantity of unique particulate tracers aswell as the associated financial cost, time, equipment, and personnel tohandle the large quantity of the unique particulate tracers.Furthermore, quantitative evaluation of stage and/or stage groupcontribution to flow is not generally possible with the existing mannerthat the unique particulate tracers are placed throughout the entiretyof stages and/or stage groups. First, in FIGS. 1E-1, 1E-2, and 1E-3 ,quantitative evaluation of stage or stage group contribution to flow isnot generally possible because the particulate tracers of wellbore 120may go to one or both offset wellbores 175. As a result, the particulatetracers affecting the flow in the wellbore 120 may not be known andthere may not be a good baseline for flow profiling. As another example,tracer recovery curves may simply indicate a binary response of flow vsno-flow. FIG. 1G illustrates a single wellbore with a StageM and aStageN and FIG. 1H illustrates typical tracer recovery curves indicativeof just the binary response of flow vs. no-flow. Second, tracer releaserate is not a function of the flowrate, so the quantification isgenerally not possible with the existing tracer design. Indeed, existingplacement of unique particulate tracers have not been able to quantifythe flow profile along the lateral during flow so far because tracerrelease rate for unique particulate tracers is not proportional to theflow rate. For example, the existing practice of placing uniqueparticulate tracers throughout the entirety of stages and/or stagegroups make it difficult to quantify the flow profile along the lateralduring flow because tracer release rate for particulates is notproportional to the flow rate. Third, if the unique particulate tracersare distributed throughout the injected stage volume, then the producedunique particulate tracer response may be very dispersed so the existingmethods (similar to solid wellbore tracer application) for flowprofiling called the pulse velocity method or decay method cannot beused. In short, there are current limitations on flow profiling usingunique particulate tracers that are placed in the entirety of stagesand/or stage groups.

In contrast to the existing practice of placing unique particulatetracers, in the example embodiments of the present disclosure the uniqueparticulate tracers are pumped only in a fraction of each stage suchthat a substantial portion of the unique particulate tracers are placedin a near wellbore region of the subsurface formation proximate to thewellbore. FIGS. 2A, 2B, and 2C illustrate non-limiting embodiments ofplacing unique particulate tracers in a subterranean formation having awellbore therewithin consistent with the instant disclosure. In FIGS.2A, 2B, and 2C, the proppant 112 is pumped in the entirety of eachStage1 through StageN for the single wellbore 120 as in FIGS. 1D-1,1D-2, and 1D-3 . However, unique particulate tracers 170 (illustrated as170 a _(oil), 170 b _(oil), and so on) are pumped only in a fraction ofeach stage such that a substantial portion of the unique particulatetracers 170 are placed in a near wellbore region 180 (illustrated as 180a for the near wellbore region corresponding to Stage1, 180 b for thenear wellbore region corresponding to Stage2, and so on) of thesubterranean formation 110 proximate to the wellbore 120. The uniqueparticulate tracers 170 are pumped with the proppant 112 in the nearwellbore region 180. At least one unique particulate tracer is pumped inthe fraction of each stage, and each unique particulate tracercorresponds to an oil phase, a water phase, or a gas phase.

Advantageously, a lower quantity of unique particulate tracers isutilized in embodiments consistent with the disclosure because theunique particulate tracers are placed in the near wellbore region andnot throughout each stage and/or stage group. Moreover, as will bedescribed further herein, embodiments are provided in this disclosurerelated to placing unique particulate tracers in fewer stages than allthe stages that are available, such as placing particulate tracers 170in three stages (e.g., Stage1, Stage5, and StageN) of the nine stagesthat are illustrated in FIGS. 2A, 2B, and 2C, to further decrease thequantity of unique particulate tracers that is utilized withoutsignificantly impacting the analysis.

Advantageously, the placement of the unique particulate tracers in thenear wellbore region focuses or concentrates the particulate tracers inthis area, which may increase the accuracy of flow rates that aregenerated based on the unique particulate tracers. The existing practicetypically does not provide an economic, scalable, and accurate way togenerate flow rates (e.g., absolute barrels per day) and/or flowprofiles (e.g., percentages) in unconventional long horizontal wells.Embodiments consistent with the instant disclosure may provide acost-effective, long term, non-interventional, and accurate way ofprofiling the production from individual stages of multi-stagehydraulically fractured wellbores. This may also allow for optimizationof hydrocarbon production from unconventional resources. The determinedflow rates and/or flow profiles may be utilized for completion designoptimization, understanding changes in flow profiles as a function oftime, understand rock type proximate to the wellbore, where to drill awellbore, understand production from different parts of the lateral thatcan be utilized to optimize wellbore length and/or wellbore landing,understand possible optimization equipment or techniques for increasinghydrocarbon recovery, etc. The wellbore may comprise a verticaltrajectory, a horizontal trajectory, or a deviated trajectory. Thesubterranean formation may be located onshore or located offshore.

FIG. 4 illustrates an example method of placing unique particulatetracers in a subterranean formation having a wellbore therewithinreferred to as a method 400. The unique particulate tracers may bepractically any unique particulate tracers known in the art, such asunique particulate tracers for hydrocarbons (e.g., oil), uniqueparticulate tracers for water, unique particulate tracers for gas, orany combination thereof. For example, types of particulate tracers thatare introduced into the subterranean formation may include, but are notlimited to, fluorinated benzoic acids (FBAs), fluorescein dyes,FBA/fluorescein synthesis, fluorescing nanocrystals, radioactivetracers, fluorescing nanoparticles, magnetic nanoparticle tracers, etc.

While the various steps in one embodiment of the method 400 arepresented sequentially, one of ordinary skill will appreciate that someor all of the steps may be executed in different orders, may be combinedor omitted, and some or all of the steps may be executed in parallel.Further, in one or more of the example embodiments, one or more of thesteps shown in this example method may be omitted, repeated, and/orperformed in a different order. Furthermore, a person of ordinary skillin the art will appreciate that any equations utilized herein may bemodified without changing the meaning, for example, an equation may bemodified to use different units such as metric units without changingthe meaning. A person of ordinary skill in the art will appreciate thatadditional steps not shown in FIG. 4 may be included in performing thismethod. A person of ordinary skill in the art will appreciate that fewerthan the steps shown in FIG. 4 may be used in performing this method ofpumping unique particulate tracers only in a fraction of each stage. Themethod shown in FIG. 4 is merely one embodiment that can be performed byusing a system, such as described in FIGS. 1A, 1B, 1C, and 36 .

Referring to FIG. 4 , the method 400 of FIG. 4 includes step 401 ofplacing unique particulate tracers in at least two stages, including afirst stage and a second stage, during a hydraulic fracturing operationin a subterranean formation. The unique particulate tracers are pumpedonly in a fraction of each stage such that a substantial portion of theunique particulate tracers are placed in a near wellbore region of thesubterranean formation proximate to the wellbore drilled into thesubterranean formation. At least one unique particulate tracer is pumpedin the fraction of each stage, and each unique particulate tracercorresponds to an oil phase, a water phase, or a gas phase. For example,a unique oil particulate tracer may be pumped only in a first fractionof a first stage of a stage pair and a different unique oil particulatetracer may be pumped only in a second fraction of a second stage of thestage pair. The unique particulate tracers may be pumped using existingtechniques and existing equipment as illustrated, for example, in FIGS.2A, 2B, 2C, 3A, 3B, and 3C. FIG. 4 may be applied to at least two stagesand fewer than all the stages. In the running example based on FIGS. 2Dand 7A-7G, the unique particulate tracers 170 a _(oil) and 170 e _(oil)will be placed in Stage1 in near wellbore region 180 a and Stage5 innear wellbore region 180 e, respectively. Stage1 (e.g., first stage) andStage5 (e.g., second stage) are a stage pair. The rest of FIG. 4includes different equations that may facilitate the placement of step401.

The method 400 of FIG. 4 includes step 405 to determine a minimumwellbore volume between the first stage and the second stage. In therunning example, the unique particulate tracers 170 a _(oil) and 170 e_(oil) will be placed in Stage1 and Stage5 respectively, and the minimumwellbore volume between Stage1 and Stage5 may be determined at step 405.The minimum wellbore volume may be determined using Equation 1 below.The Equation 1 is solved once of each phase.

$\begin{matrix}{{V_{{wellbore},\min}{bbls}} = {q_{\min}*t_{fs}*\frac{1}{24*60}}} & {{Equation}1}\end{matrix}$▪whereinV_(wellbore, min )isminimumwellborevolumebetweentwouniqueparticulatetracerplacements(e.g., inbbls)▪whereinq_(max)ismaximumflowrate(e.g., inbbls)▪whereint_(fs)issamplingfrequency(e.g., inminutes)${▪{Of}{note}:{If}{metric}{units}{are}{utilized}},{{then}{the}{following}{portion}{of}{Equation}1{may}{be}{omitted}:*\frac{1}{24*60}}$RunningExampleUsingEquation1:${17{bbls}} = {5000{bpd}*5{minutes}*\frac{1}{24*60}}$

The method 400 includes step 410 to determine a minimum lateral lengthbetween the first stage and the second stage. In the running example,the unique particulate tracers 170 a _(oil) and 170 e _(oil) will beplaced in Stage1 and Stage5 respectively, and the minimum lateral lengthbetween Stage1 and Stage5 may be determined at step 410. The determinedminimum wellbore volume from step 405 and a flow pipe radius (referredto as r_(w)) may be utilized to determine the minimum lateral length.The flow pipe radius may correspond to production casing or productiontubing. The minimum wellbore length may be determined using Equation 2below. The Equation 2 is solved once for each phase.

$\begin{matrix}{{L_{{wellbore},\min}{ft}} = \frac{V_{{wellbore},\min}}{\pi r_{w}^{2}}} & {{Equation}2}\end{matrix}$▪whereinL_(wellbore, min )isminimumlaterallengthbetweentwouniqueparticulatetracerplacements(e.g., infeet)▪whereinr_(w)isaflowpiperadius(e.g., wellborediameterininches)RunningExampleUsingEquation2:${591{feet}} = \frac{17{bbls}}{{\pi 5}\text{.5}{inches}^{2}}$

Parameters on which the tracer placement for flow profiling depend areprovided and these are utilized in the Equations 1-2 hereinabove: (a)max expected flowrate from the well: q_(max) bbls/day, and (b) fastestsampling frequency at surface post shut-in possible at the surface(t_(fs) minutes): such as 5-minute interval. Moreover, this uniquetracer placement at the above minimum lateral length may allow forobtaining non-overlapping signals at the surface at the practicalsampling frequency of 1 sample every 5 minutes.

The method 400 includes step 415 to determine a quantity of stageswithout unique particulate tracers between the first stage and thesecond stage. In the running example, the unique particulate tracerswill not be placed in three stages (i.e., Stage2, Stage3, and Stage4 inFIG. 2D) using the minimum lateral length between Stage1 and Stage5 thatwas determined at step 410. The quantity of stages without uniqueparticulate tracers may be determined using Equation 3 below. TheEquation 3 is solved once for each phase.

$\begin{matrix}{{{quantity}{of}{stages}{without}{unique}{particulate}{tracers}{between}{two}{unique}{particulate}{tracer}{placements}} = \frac{L_{{wellbore},\min}}{Lstage}} & {{Equation}3}\end{matrix}$▪whereinL_(wellbore, min )isminimumlaterallengthbetweentwouniqueparticulatetracerplacements(e.g., infeet)▪whereinLstageisstagelength(e.g., infeet) RunningExampleUsingEquation3:${3{stages}} = \frac{591{feet}}{200{feet}}$

The method 400 includes step 420 to determine a maximum fluid volume ina stage near the wellbore that is in contact with a unique particulatetracer, which will be utilized later herein to determine a fraction ofeach stage in which to pump a unique particulate tracer. If the uniqueparticulate tracers are placed inside the subterranean formation withproppant, and the stage in which the tracers are placed does not flow ata sufficient rate, then the particulate tracer signals would overlapinside the wellbore and would not stay distinct, which is used for flowprofiling. Thus, minimum flowrate q_(min,stage) (e.g., bbls/day) from astage is a design parameter to determine tracer placement within thestage. The maximum fluid volume in a stage near the wellbore that is incontact with a unique particulate tracer may be determined usingEquation 4 below. The Equation 4 is solved once for each phase.

$\begin{matrix}{{V_{p}{bbls}} \leq {q_{\min,{stage}}*\frac{t_{fs}}{24*60}}} & {{Equation}4}\end{matrix}$▪whereinV_(p)isamaximumfluidvolumeinastagenearthewellborethatisincontactwithuniqueparticulatetracer(e.g.inbbls)▪whereinq_(min , stage)inminimumflowratefromastage(e.g., inbbls)▪whereint_(fs)issamplingfrequency(e.g., inminutes)(e.g.,  ∼ 5minutes)Ofnote : Ifmetricunitsareutilized, thenthefollowingportionofEquation4maybeomitted : 24 * 60RunningExampleUsingEquation4:${1.041667{bbls}} \leq \ {300{bpd}*\frac{5{minutes}}{24*60}}$

The method 400 includes step 425 to determine proppant pack bulk volume,which will be utilized later herein to determine a fraction of eachstage in which to pump a unique particulate tracer. The correspondingproppant packing bulk volume, V_(bulk-proppant), if the proppant packporosity is Ø, may be determined using Equation 5 below. The Equation 5is solved once for each phase.

$\begin{matrix}{V_{{bulk} - {proppant}},{{bbls} = {\frac{V_{p}}{\varnothing}*\left( {1 - \varnothing} \right)}}} & {{Equation}5}\end{matrix}$whereinV_(bulk − proppant)isproppantpackbulkvolume(e.g., inbbls)whereinV_(p)isamaximumfluidvolumeinstagenearthewellborethatisincontactwithuniqueparticulatetracer(e.g., inbbls)wherein⌀isproppantpackporosity RunningExampleUsingEquation5:${2.430556{bbls}} = {\frac{1.041667}{0.3}*\left( {1 - {{0.3}0}} \right)}$

The method 400 includes step 430 to determine proppant mass tagged witha unique particulate tracer if proppant density is ρ_(proppant) (e.g.,lbs/gallon), which will be utilized later herein to determine a fractionof each stage in which to pump a unique particulate tracer. Taggedrefers to includes as in what is the proppant mass that includes aunique particulate tracer. The proppant mass tagged with uniqueparticulate tracer may be determined using Equation 6 below. TheEquation 6 is solved once for each phase (add claim).

$\begin{matrix}{{{tagged}{proppant}{mass}},{{lbs} = {42*V_{{bulk} - {proppant}}*\rho_{proppant}}}} & {{Equation}6}\end{matrix}$whereintaggedproppantmassisproppantmasstaggedwiththeuniqueparticulatetracers(e.g., inlbs)whereinV_(bulk − proppant)isproppantpackbulkvolume(e.g., inbbls)whereinρ_(proppant)isproppantdensity(e.g., lbs/gallon)Ofnote : Ifmetricunitsareutilized, thenthefollowingportionofEquation6maybeomitted : 42*RunningExampleUsingEquation6:${2256.144{lbs}} = {42*{2.4}30556bbls*22\frac{lb}{gal}}$Ofnote : ρ_(proppant)of22lb/galwasdeterminedby2.65gm/cc * 8.34.

The method 400 includes step 435 to determine proppant pumped in astage, which will be utilized later herein to determine a fraction ofeach stage during which to pump a unique particulate tracer. Duringfracture design, each stage gets completed with M_(p,stage) (e.g., lbs)of proppant. The proppant pumped in a stage may be determined usingEquation 6 below. The Equation 7 is solved once, and substantially thesame answer is utilized for each phase.

$\begin{matrix}{{M_{p,{stage}}{lbs}} = {{proppant}{intensity}*L_{stage}}} & {{Equation}7}\end{matrix}$ whereinM_(p, stage)isproppantpumpedinastage(e.g., inlbs)whereinproppantintensitymaybeexpressedaslb/ftwhereinL_(stage)islengthofstage(e.g., inches)RunningExampleUsingEquation7:${440000{lbs}} = {2000\frac{lb}{ft}*200{feet}}$

The method 400 includes step 440 to determine a fraction of a stage inwhich to pump a unique particulate tracer. In some embodiments, afraction comprises 0.001% to 10%. In some embodiments, a fractioncomprises 0.001% to 25%. In some embodiments, a fraction comprises0.001% to 50%. In some embodiments, the same fraction may be utilizedfor each stage. The fraction of a stage in which to pump a uniqueparticulate tracer may be determined using Equation 8 below: TheEquation 8 is solved once for each phase.

$\begin{matrix}{{{fraction}{of}{stage}{tagged}{with}a{unique}{particulate}{tracer}} = \ \frac{{{Tagged}{proppant}{mass}},{lbs}}{M_{pstage}lbs}} & {{Equation}8}\end{matrix}$whereinfractionofstagetaggedwithauniqueparticulatetracerispercentageofastagewhereintaggedproppantmassisproppantmasstaggedwithauniqueparticulatetracer(e.g., inlbs)whereinM_(p, stage)isproppantpumpedinastage(e.g., inlbs)RunningExampleUsingEquation8:${0.0051{percent}{of}{stage}{tagged}{with}a{unique}{particulate}{tracer}} = \frac{2256.144{lbs}}{440000{lbs}}$Ofnote : 0.0051mayberepresentedas0.51⁠%ofstagetaggedwithauniqueparticulartracer

In the running example, the fraction is a percentage of the stage suchas 0.51% of the stage, and the whole stage is 100%. Regarding steps 430,435, and 440, in the running example, about 2256.144 lbs of the proppant112 will be tagged with the unique particulate tracer 170 a _(oil) in0.51% (i.e., fraction) of Stage1 out of about 440,000 lbs of theproppant 112 that will be pumped into the Stage1. Existing practicewould have added particulate tracers throughout the 440,000 lbs ofproppant in Stage1. Similarly, about 2256.144 lbs of proppant 112 willbe tagged with the unique particulate tracer 170 e _(oil) in 0.51%(i.e., fraction) of Stage5 out of the about 440,000 lbs of the proppant112 that will be pumped into the Stage5. Thus, this running exampleillustrates a substantial reduction in the quantity of uniqueparticulate tracers that will be utilized in Stage1 and Stage5. Thefraction of 0.51% may translate to about 1 minute of pumping time.

The method 400 includes a step 445 to pump a proppant mass that istagged with a unique particulate tracer in a fraction of each stage foreach phase. The unique particulate tracer is pumped in the determinedfraction at the start and/or at the end of a stage injection such that asubstantial portion of the unique particulate tracer is placed in a nearwellbore region of the subterranean formation proximate to the wellboreof the corresponding stage. Start of stage injection: Based on somegeomechanical models, early in the stage injected proppant stays closeto the wellbore. End of stage injection: Conventional thinking is thatthe proppant injected at the end stays close to the wellbore. In therunning example, the 2256.144 lbs of the proppant 112 tagged with theunique particulate tracer 170 a _(oil) may be pumped in 0.51% (i.e.,fraction) of Stage1 at the start of the stage injection or at the end ofstage injection such that the proppant 112 tagged with the uniqueparticulate tracer 170 a _(oil) is pumped into the near wellbore region180 a. In the running example, the 2256.144 lbs of the proppant 112tagged with the unique particulate tracer 170 e _(oil) may be pumped in0.51% (i.e., fraction) of Stage5 at the start of the stage injection orat the end of stage injection such that the proppant 112 tagged with theunique particulate tracer 170 e _(oil) is pumped into the near wellboreregion 180 e. Pumping of the fraction of a stage with proppant masstagged with the unique particulate tracer at the start/end of stagetreatment will allow for the tracer to be placed in the near wellboreregion.

For pumping, a unique particulate tracer may be kept in an isolationtank and the proppant may be kept in a different isolation tank, andthen both get added to the fracturing fluid and the fracturing fluid isinjected. Separate pumps for the proppant and the the unique particulatetracer may be utilized until they are mixed in the stream (e.g., streamof fracturing fluid). Afterwards, there may be other pumps that furtherpressurize the mix to be pumped into the wellbore.

Additional information: The particulate tracer placement designdiscussed before allows for the tracer dilution between the volumecontained between the locations/stages where the two unique particulatetracers are placed V_(wellbore,min) bbls is mixed with the volume offluid flowing from the stage downstream V_(p) bbls because the placementis designed such that the time it takes for the fluid to flow in thewellbore from upstream (e.g., location closer to the wellbore's toe) todownstream (e.g., location closer to the wellbore's heel) is less thanequal to time it would take particulate contacted volume downstream toflow into the wellbore and mix with the total stream. This would also bethe maximum dilution that the tracer would undergo in theory and wouldbe what would be observed at the surface. This is illustrated in FIG. 5.

The method 400 includes step 450 to determine surface tracerconcentration. This relationship is used to determine the amount ofunique particulate tracer mass to be injected. In one embodiment, thetracer concentration observed at the surface should at least be theequivalent to the tracer quantification limit as determined by aconventional lab analytical method. For most unique particulate tracerssuch a limit is ˜5 ppb. In one embodiment, a phase amplification factormay also be incorporated while using this relationship to determine theunique particulate tracer mass design. The surface tracer concentrationmay be determined using equation 9 below. The surface observed tracerconcentration with dilution would be Equation 9. The Equation 9 issolved once for each phase.

$\begin{matrix}{{{Tracer}{{conc}.{@{surface}}}},{{ppb} = {\frac{{{P{articulate}}{tracer}{mass}{released}{from}V_{p}},{lbs}}{{{Mass}{of}{fluid}{in}\left( {V_{{wellbore},\min} + V_{p}} \right)},{lbs}}*10^{9}}}} & {{Equation}9}\end{matrix}$

The method 400 includes step 455 to determine a dilution amplificationfactor. In one embodiment, the dilution amplification factor could bethe ratio of wellbore volume between two tracer placements to the totalwellbore volume because it removes any dilution related uncertainty thatcould be a part of the design. The dilution amplification factor may bedetermined using Equation 10 below. The Equation 10 is solved once foreach phase.

$\begin{matrix}{{{Dilution}{amplification}{factor}} = \frac{\left( {{Total}{wellbore}{volume}\left( {V_{{wellbore},{total}}b{bls}} \right)} \right)}{\begin{matrix}{{Min}{Wellbore}{volume}{between}{two}} \\{{particulate}{tracer}{placement}\left( {V_{{wellbore},\min}{bbls}} \right)}\end{matrix}}} & {{Equation}10}\end{matrix}$ RunningExampleUsingEquation10:$26 = \frac{450{bbls}}{17{bbls}}$

The method 400 includes step 460 to determine particulate tracer massreleased, which is a minimum to be released in the subsurface in orderto see at least 5 ppb in the surface. The tracer mass in the particulatecontacted volume V_(p) using the below constraint (detection,quantification limit) from laboratory analysis: The Equation 11 issolved once for each phase.

Tracer conc.@surface,ppb≥Detection,quantification limit,ppb  Equation11:

With tracer release rate from a unique particulate tracer measured inthe lab, the actual mass of a unique particulate tracer to be injectedin the fraction of a stage in the improved configuration could bedetermined. The expected tracer release rate plot is shown in FIG. 6 .The detection, quantification limit may be 5 ppb in one embodiment. Thedetection, quantification limit may be in a range of 0.1 ppb to 100 ppb.In another embodiment, the detection, quantification limit may be in arange of 0.1 ppb to 10 ppb in another embodiment. The detection,quantification limit may be 5 ppb or higher in another embodiment. Inone embodiment, the detection, quantification limit may even be 0.1 ppbor lower. The particulate tracer mass released may be determined usingEquation 12 below. The Equation 12 is solved once for each phase.

$\begin{matrix}{{{unique}{particulate}{tracer}{mass}{released}},{{lbs} = \frac{\begin{matrix}{{Detection},{{quantification}{limit}},{{ppb}*}} \\{{Mass}{of}{fluid}{in}\left( {V_{{wellbore},\min} + V_{p}} \right)*} \\{{Dilution}{{Amp}.{factor}}}\end{matrix}}{10^{9}}}} & {{Equation}12}\end{matrix}$whereinTracerconc.@surface, ppb ≥ Detection, quantificationlimit, ppb${{Of}{note}:{The}{Equation}12{uses}{concentration}{in}{ppb}{so}{we}{multiply}{the}{RHS}{by}{10\hat{}9}},{{but}{if}{we}{use}{the}{concentration}{}{in}{ppm}{then}{we}{would}{multiply}{RHS}{by}{10\hat{}6.}{Alternatively}},{{if}{we}{use}{ceoncentration}{as}{true}{fraction}/{ratio}{then}{we}{would}{not}{multiply}{}{RHS}{with}{just}1.}$RunningExampleUsingEquation12:${0.000835418{lbs}} = \frac{5{ppb}*6446.125{lbs}*26}{10^{9}}$whereinTracerconc.@surface, ppb ≥ 5ppb

The method 400 includes step 465 to determine design particulate mass.The amount of tracer released from the particulate tracers is a functionof the injected tracer mass as well as the exposure time of the tracerto the fluid which could be seen from the release rate. A typical wellshut-in duration t_(shutin) is ˜24 hours so the tracer concentrationcould be built for analysis would lead to the following particulate massfor injection using the release rate @T_(min_usable_tracer_release_rate) so the design would still work fortime less than T_(min_usable_tracer_release_rate) because the releaserates would be higher for those times. The Equation 13 is solved oncefor each phase.

$\begin{matrix}{{{Design}{particulate}{mass}},{{lbs} = \frac{{t_{shutin}*{particulate}{tracer}{mass}{released}},{lbs}}{\begin{matrix}{24*{\min.{usable}}{tracer}{mass}{released}{{rate}@}} \\{T_{\min\_{usable}\_{tracer}\_{release}\_{rate}}\left( \frac{\frac{lbs}{lbs}}{day} \right)}\end{matrix}}}} & {{Equation}13}\end{matrix}$Ofnote : Theequationcouldhavethe24removedfromthedenominatorifeverythingelseisinstandardunits.RunningExampleUsingEquation13:${22{lbs}} = \frac{24*0.000835418{lbs}}{{24*{3.7}9735E} - {05\left( \frac{\frac{lbs}{lbs}}{day} \right)}}$

The method 400 includes step 470 to determine design particulate mass totagged proppant ratio. The Equation 14 is solved once for each phase.

$\begin{matrix}{{{Design}{particulate}{mass}{to}{tagged}{proppant}{ratio}} = \ \frac{{{Design}{particulate}{mass}},{lbs}}{{T{agged}{proppant}{{mas}s}},{lbs}}} & {{Equation}14}\end{matrix}$ RunningExampleUsingEquation14:$0.009751152\  = \ \frac{22lbs}{225{6.1}44lbs}$

The method 400 includes step 475 to handle multi-phase flow dilution.With phase amplification factor introduced in the design, the producedtracer concentrations would still be at quantification limit as long asthe WOR is equal to or greater than the phase amplification factor forwater tracers and vice versa for oil tracers. The Equation 15 is solvedonce for each phase.

Water particulate tracer surface concentrations≥Quantifiable Limit ifWOR≥Phase Amplification Factor  Equation 15:

With large phase amplification factors, if the water or oil tracer fallbelow detectable limit, the flowrate of the respective phase is smallcompared to the other phase and thus should be the main flow phase ofconcern. The Equation 16 is solved once for each phase.

$\begin{matrix}{{{Oil}{particulate}{tracer}{surface}{concentrations}} \geq {{{Quantifiable}{Limit}{if}}{WOR}} \geq \frac{1}{{Phase}{Amplification}{Factor}}} & {{Equation}16}\end{matrix}$

The improved implementation of unique particulate tracers with thedesign methodology outlined is similarly applicable to both oil andwater particulate tracers. With oil and water flowing simultaneously,the way the improved application is designed would account for reductionin the tracer mass for oil or water and a corresponding increase in thetracer mass for water or oil if contact area changes between water andoil particulate tracers and its corresponding reduction in the tracerconcentration because overall flowrate of the corresponding phase alsogoes down along with the dilution.

Each of the following items are incorporated by reference: (1) Jain,Lokendra, Doorwar, Shashvat, and Daniel Emery. “Analytical TracerInterpretation Model for Fracture Flow Characterization and Swept VolumeEstimation in Unconventional Wells.” Paper presented at the SPE/AAPG/SEGUnconventional Resources Technology Conference, Houston, Tex., USA, July2021; (2) U.S. Pat. No. 8,949,029; (3) Haitao Li, et al., Evaluation ofthe Release Mechanism of Sustained-Release Tracers and its Applicationin Horizontal Well Inflow Profile Monitoring, ACS Omega 2021 6 (29),19269-19280; and (4) Flow loop testing to validate Tracerco's solidchemical inflow tracer technology, Tracerco Limited, 2021, available athttps://www.tracerco.com/downloads/case-studies/flow-loop-testing-to-validate-tracercos-solid-chemical-inflow-tracer-technology/.

One or more of the steps described hereinabove in the method 400 of FIG.4 may be implemented by a system and/or in a system, such as a system3600 shown in FIG. 36 as illustrated in FIG. 8 . For example, the step405 to determine a minimum wellbore volume between the first stage andthe second stage may be implemented by component 804 in FIG. 8 . Thestep 410 to determine a minimum lateral length between the first stageand the second stage may be implemented by component 806 in FIG. 8 . Thestep 440 to determine a fraction of a stage in which to pump a uniqueparticulate tracer may be implemented by component 808 in FIG. 8 . Arepresentation of one or more of the values determined in the method 400of FIG. 4 may be generated and displayed by component 810.

Determining a Flow Profile for a Wellbore Using Unique ParticulateTracers that are Pumped Only in a Fraction of Each Stage Such that aSubstantial Portion of the Unique Particulate Tracers are Placed in aNear Wellbore Region of the Subterranean Formation Proximate to theWellbore:

Reference will now be made in detail to various embodiments, examples ofwhich are illustrated in the accompanying drawings. In the followingdetailed description, numerous specific details are set forth in orderto provide a thorough understanding of the present disclosure and theembodiments described herein. However, embodiments described herein maybe practiced without these specific details. In other instances,well-known methods, procedures, components, and mechanical apparatushave not been described in detail so as not to unnecessarily obscureaspects of the embodiments.

Example embodiments of determining a flow profile for a wellbore usingunique particulate tracers will be described more fully hereinafter withreference to the accompanying drawings. The unique particulate tracersare pumped in at least one stage pair during a hydraulic fracturingoperation performed in the subterranean formation, and wherein theunique particulate tracers are pumped only in a fraction of each stagesuch that a substantial portion of the unique particulate tracers areplaced in a near wellbore region of the subterranean formation proximateto the wellbore. At least one unique particulate tracer is pumped in thefraction of each stage, and each unique particulate tracer correspondsto an oil phase, a water phase, or a gas phase. However, determining aflow profile may be embodied in many different forms and should not beconstrued as limited to the example embodiments set forth herein.Rather, these embodiments and examples are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of determining a flow profile to those of ordinary skill in theart. Like, but not necessarily the same, elements (also sometimes calledcomponents) in the various figures are denoted by like referencenumerals for consistency.

FIG. 9 illustrates an example method of determining a flow profile for awellbore using unique particulate tracers referred to as a method 900.The unique particulate tracers may be practically any unique particulatetracers known in the art, such as unique particulate tracers forhydrocarbons (e.g., oil), unique particulate tracers for water, uniqueparticulate tracers for gas, or any combination thereof. For example,types of particulate tracers that are introduced into the subterraneanformation may include, but are not limited to, fluorinated benzoic acids(FBAs), fluorescein dyes, FBA/fluorescein synthesis, fluorescingnanocrystals, radioactive tracers, fluorescing nanoparticles, magneticnanoparticle tracers, etc.

While the various steps in one embodiment of the method 900 arepresented sequentially, one of ordinary skill will appreciate that someor all of the steps may be executed in different orders, may be combinedor omitted, and some or all of the steps may be executed in parallel.Further, in one or more of the example embodiments, one or more of thesteps shown in this example method may be omitted, repeated, and/orperformed in a different order. Furthermore, a person of ordinary skillin the art will appreciate that any equations utilized herein may bemodified without changing the meaning, for example, an equation may bemodified to use different units such as metric units without changingthe meaning. A person of ordinary skill in the art will appreciate thatadditional steps not shown in FIG. 9 may be included in performing thismethod. A person of ordinary skill in the art will appreciate that fewerthan the steps shown in FIG. 9 may be used in performing this method ofdetermining a flow profile for a wellbore using unique particulatetracers. The method shown in FIG. 9 is merely one embodiment that can beperformed by using a system, such as described in FIGS. 1A, 1B, 1C, and36.

Referring to FIG. 9 , the method 900 of FIG. 9 includes step 901 toobtain produced fluid samples comprising unique particulate tracers froma wellbore drilled into a subterranean formation. The unique particulatetracers are pumped in at least one stage pair (e.g., a first stage and asecond stage) during a hydraulic fracturing operation performed in thesubterranean formation. The unique particulate tracers are pumped onlyin a fraction of each stage such that a substantial portion of theunique particulate tracers are placed in a near wellbore region of thesubterranean formation proximate to the wellbore. At least one uniqueparticulate tracer is pumped in the fraction of each stage, and whereineach unique particulate tracer corresponds to an oil phase, a waterphase, or a gas phase. Practically any known technique or knownequipment may be utilized to obtain the produced fluid samples.

The method 900 of FIG. 9 includes step 905 to obtain a tracerconcentration history for each unique particulate tracer, for example,as described herein.

The method 900 of FIG. 9 includes step 910 to determine a wellborevolume for the stage pair. In one embodiment, the wellbore volume isdetermined using an equation as follows:

V _(wellbore) =L _(wellbore) ft*πr _(w) ²

wherein V_(wellbore) is wellbore volume, L_(wellbore)ft is length for aspecific stage pair (e.g., length between a first stage and a secondstage of a stage pair), and r_(w) is a flow pipe radius. The wellborevolume may be solved once, and substantially the same answer may bereused for various stage pairs.

The method 900 of FIG. 9 includes step 915 to determine a flow profilefor the wellbore for each phase indicative of flow contribution for eachstage pair and stages in between each stage pair using the wellborevolume and the corresponding tracer concentration histories. In oneembodiment, the flow contribution is determined using an equation asfollows:

$q_{N,{{bbls}/{day}}} = \frac{V_{{wellbore},N},{({bbls})*24*60}}{{\Delta t},{minutes}}$

wherein q_(N,bbls/day) is flow contribution for a specific stage pair,V_(wellbore) is wellbore volume, Δt is arrival time difference, and N isa specific stage. For example, as in FIG. 2D, a stage pair includes afirst stage that received unique particulate tracer 170 a _(oil) and asecond stage that received unique particulate tracer 170 e _(oil), withthree stages are located between the first stage and the second stagewithout any unique particulate tracers. Thus, the flow contribution mayinclude the stage pair of the first stage and the second stage as wellas the three stages in between. FIG. 10 provides more informationincluding the Δt, which is arrival time difference. With the improvedplacement and design, the particulate tracer response at the surfacecould be interpreted like wellbore solid tracers for flow profiling asillustrated in FIG. 10 .

The method 900 of FIG. 9 includes step 920 as a check by obtaining aproduction history for the wellbore; summing all flow contributions foreach stage pair for each phase; and comparing the sums and theproduction history to constraint total flow contribution for each phase.The production history may be obtained as discussed elsewhere herein.This step may be performed as a check.

If there is an inconsistency, then the method 900 may include anoptional step 925 to smooth a tracer concentration history for aspecific unique particulate tracer before c) of step 915 to reduce noise(e.g., reduce points that show large variations ups and/or downs); andutilize the smoothed tracer concentration history for the specificunique particulate tracer in c) of step 915. This optional step 915 maybe performed by curve fitting to smoothen out the data (e.g., normal,log normal, or other representative curve fit).

The method 900 of FIG. 9 includes step 930 to generate, on a graphicaluser interface, a representation of the flow profile for the wellborefor each phase indicative of the flow contribution for each stage pairand stages within each stage pair; and display, via the graphical userinterface, the representation.

Those of ordinary skill in the art will appreciate that variousmodifications may be made to the description above. For example, themethod 900 may include an optional step 935 to refine the wellborevolume in response to multiple phases in the wellbore. Various ways torefine the wellbore volume are provided in FIGS. 11-22 . Various otheroptional steps are also provided in FIGS. 11-22 .

One or more of the steps described hereinabove in the method 900 of FIG.9 may be implemented by a system and/or in a system, such as a system3600 shown in FIG. 36 as illustrated in FIG. 23 . For example, the step905 to obtain a tracer concentration history for each unique particulatetracer may be implemented by component 2304 in FIG. 23 . The step 910 todetermine a wellbore volume for the stage pair may be implemented bycomponent 2306 in FIG. 23 . The step 915 to determine a flow profile forthe wellbore for each phase indicative of flow contribution for eachstage pair and stages in between each stage pair using the wellborevolume and the corresponding tracer concentration histories may beimplemented by component 2308 in FIG. 23 . A representation of one ormore flow profiles may be generated and displayed by component 2310.FIG. 7A-7G include various examples consistent with the disclosure.

Comparison Between Solid Wellbore Tracer vs Concentrated ParticulateTracers: In a typical wellbore with 3 inch id, the surface area per ftfor wellbore tracers is 0.8 ft2. If installed over two tubing lengths(60 ft). the exposed surface area is 48 ft2. If the wellbore tracer isinstalled over a stage of 200 ft in length, the exposed surface area is160 ft2. 1 gm particulate tracers have exposed surface area of 32000 ft2and occupies 0.00017 ft3 of the volume. Over a length of 1 ft and ˜2000lbs of proppant loading in the reservoir and random closed packing has apore volume of ˜19 ft3 and bulk volume of ˜12 ft3 so a tracer loading of1 kg of tracer in last 10% of the stage with 1.2 ft3 of near wellborebulk volume would occupy 0.17 ft3 which would end up providing theexposed surface area of 32*10{circumflex over ( )}6 ft2. The maximumfluid contacted volume in the last 10% of a stage with abovespecifications would be 1.9 ft3 per ft of a stage. For a stage with thelength of 200 ft, the tracer contacted volume could be ˜67 bbls withlarge exposed tracer surface area as calculated. This would allow for asignificant tracer concentration spike 6 orders of magnitude higher thanthe conventional wellbore tracers and should also act similar towellbore tracers to estimate flowrate across the well using pulsevelocity method. The technique would use high frequency sampling likefor a deepwater well and equivalent to 24 to 48 hours. These tracersshould also last a while but the life span would be smaller 10 timessmaller (6 to 12 months, field observation) than the conventionalwellbore tracers (upto 5 years). Non-interventional, allows fordetermining water breakthrough stages, allows for oil/water ratequantification for stages over time, allows for same tracers to beinstalled in multiple wells nearby because we can focus on the tracerflowback with pulse velocity method.

Determining a Flow Profile for a Wellbore Using Unique ParticulateTracers that are Pumped Throughout Each Stage, Each Stage Group, or anyCombination Thereof:

Reference will now be made in detail to various embodiments, examples ofwhich are illustrated in the accompanying drawings. In the followingdetailed description, numerous specific details are set forth in orderto provide a thorough understanding of the present disclosure and theembodiments described herein. However, embodiments described herein maybe practiced without these specific details. In other instances,well-known methods, procedures, components, and mechanical apparatushave not been described in detail so as not to unnecessarily obscureaspects of the embodiments.

Example embodiments of determining a flow profile for a wellbore usingunique particulate tracers will be described more fully hereinafter withreference to the accompanying drawings. At least one unique particulatetracer is pumped throughout each stage, each stage group, or anycombination thereof during a hydraulic fracturing operation performed inthe subterranean formation in example embodiments, however, determininga flow profile may be embodied in many different forms and should not beconstrued as limited to the example embodiments set forth herein.Rather, these embodiments and examples are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of determining a flow profile to those of ordinary skill in theart. Like, but not necessarily the same, elements (also sometimes calledcomponents) in the various figures are denoted by like referencenumerals for consistency.

As explained hereinabove, in the existing practice, as illustrated inFIGS. 1D-1, 1D-2, 1D-3, 1E-1, 1E-2, and 1E-3 , quantitative evaluationof stage and/or stage group contribution to flow is not generallypossible with the existing manner that unique particulate tracers areplaced throughout the entirety of stages and/or stage groups. First, inFIGS. 1E-1, 1E-2 , and 1E-3, quantitative evaluation of stage and/orstage group contribution to flow is not generally possible because theunique particulate tracers of wellbore 120 may go to one or both offsetwellbores 175. As a result, the unique particulate tracers affecting theflow in the wellbore 120 may not be known and there may not be a goodbaseline for flow profiling. As another example, tracer recovery curvesmay simply indicate a binary response of flow vs no-flow. FIG. 1Gillustrates a single wellbore with a StageM and a StageN, and FIG. 1Hillustrates typical tracer recovery curves indicative of just the binaryresponse of flow vs. no-flow. Second, tracer release rate is not afunction of the flowrate, so the quantification is generally notpossible with the existing tracer design. Indeed, existing placement ofunique particulate tracers have not been able to quantify the flowprofile along the lateral during flow so far because tracer release ratefor unique particulate tracers is not proportional to the flow rate. Forexample, the existing practice of placing unique particulate tracersthroughout the entirety of stages and/or stage groups make it difficultto quantify the flow profile along the lateral during flow becausetracer release rate for particulates is not proportional to the flowrate. Third, if the unique particulate tracers are distributedthroughout the injected stage volume, then the produced uniqueparticulate tracer response may be very dispersed so the existingmethods (similar to solid wellbore tracer application) for flowprofiling called the pulse velocity method or decay method cannot beused. In short, there are current limitations on flow profiling usingunique particulate tracers that are placed in the entirety of stagesand/or stage groups.

Advantageously, as will be described further herein, embodiments areprovided in this disclosure related to determining a flow profile for awellbore using unique particulate tracers that are pumped throughouteach stage, each stage group, or any combination thereof. By doing so,these embodiments may be utilized to provide quantitative flow profilesthat were not generally available in the existing practice. Furthermore,provided herein are embodiments of two methods referred to as the“response time delay method” and the “decline method” that may beutilized to determine the flow profiles. The “response time delaymethod” may be dependent on the release rate, but the “decline method”is not. In some circumstances, both the “response time delay method” andthe “decline method” may be utilized for comparison and validation.

Advantageously, embodiments provided herein may be utilized fornon-interventional time-based flow profiling using the uniqueparticulate tracers. The determined flow profiles may be utilized forcompletion design optimization, understanding changes in flow profilesas a function of time, understand rock type proximate to the wellbore,where to drill a wellbore, understand production from different parts ofthe lateral that can be utilized to optimize wellbore length and/orwellbore landing, understand possible optimization equipment ortechniques for increasing hydrocarbon recovery, etc.

Response Time Delay Method:

The methods and systems of the present disclosure may be implemented bya system and/or in a system, such as a system 3600 shown in FIG. 36 andFIG. 24 . A method of determining a flow profile for a wellbore usingunique particulate tracers may be performed by the processor 3618,including input such as at least one tracer concentration history (e.g.,a tracer concentration history for each unique particulate tracer)and/or a production history for a wellbore as well as output such as aflow profile for the wellbore for each phase indicative of flowcontribution of each stage, each stage group, or any combinationthereof. The electronic storage 3622 may store information relating tothe tracer concentration history for each unique particulate tracer, theproduction history of the wellbore, information about the produced fluidsamples, and/or other information. The graphical display 3624 maypresent information relating to the flow profile for the wellbore foreach phase indicative of the flow contribution of each stage, each stagegroup, or any combination thereof, and/or other information.

The processor 3618 may be configured to execute one or moremachine-readable instructions 3602 to facilitate determining the flowprofile for the wellbore for each phase using the unique particulatetracers. The machine-readable instructions 3602 may include one or morecomputer program components. The machine-readable instructions 3602 mayinclude a tracer concentration history component 2404, a productionhistory component 2406, a mean residence time component 2408, a contactvolume proxy component 2410, a flow profile component 2412, a smoothingcomponent 2414, a representation component 2416, and/or other computerprogram components.

The tracer concentration history component 2404 may be configured toobtain (e.g., from the non-transitory storage medium such as theelectronic storage 3622) a tracer concentration history for each uniqueparticulate tracer in produced fluid samples from a wellbore drilledinto a subterranean formation. At least one unique particulate tracerwas pumped throughout each stage, each stage group, or any combinationthereof during a hydraulic fracturing operation performed in thesubterranean formation. Each unique particulate tracer corresponds to anoil phase, a water phase, or a gas phase. The produced fluid samplescomprise at least a portion of the unique particulate tracers that arepumped throughout the stages, the stage groups, or any combinationthereof.

The production history component 2406 may be configured to obtain (e.g.,from the non-transitory storage medium such as the electronic storage3622) a production history for the wellbore.

The mean residence time component 2408 may be configured to determine(e.g., with the physical computer processor such as the processor 3618)a mean residence time for each unique particulate tracer using thecorresponding tracer concentration history.

The contact volume proxy component 2410 may be configured to determine(e.g., with the physical computer processor such as the processor 3618)a contact volume proxy for each unique particulate tracer using theproduction history and the corresponding tracer concentration history.

The flow profile component 2412 may be configured to determine (e.g.,with the physical computer processor such as the processor 3618) a flowprofile for the wellbore for each phase indicative of flow contributionof each stage, each stage group, or any combination thereof by using thecorresponding mean residence times and the corresponding contact volumeproxies.

The smoothing component 2414 may be configured to smooth (e.g., with thephysical computer processor such as the processor 3618) a tracerconcentration history for a specific unique particulate tracer beforedetermining a mean residence time and before determining a contactvolume proxy to reduce noise. The smoothed tracer concentration historyfor the specific unique particulate tracer may be utilized indetermining the mean residence time and determining the contact volumeproxy.

The representation component 2416 may be configured to generate (e.g.,on the graphical user interface such as the graphical display 3624) arepresentation of the flow profile for the wellbore for each phaseindicative of the flow contribution of each stage, each stage group, orany combination thereof. The representation component 2416 may beconfigured to display (e.g., on the graphical user interface such as thegraphical display 3624) the representation.

FIG. 25 illustrates an example method 2500 for determining a flowprofile for a wellbore using unique particulate tracers. The method 2500may be referred to as a response time delay method herein (e.g.,Response time delay, rate=volume/time), however, those of ordinary skillin the art will appreciate that this terminology is not meant to belimiting. The method 2500 may be utilized if high frequency data withmode is accurately captured with time (e.g., high frequency samplingdepending on the flow rate) and/or low oil rate. For example, theresponse delay method may be applied when data is collected in the first5 days post POP (i.e., popping the wellbore open for the first timeafter the unique particulate tracers were pumped in), such as collectingproduced fluid samples at least once a day to about 5+ a day, at leastonce a day to about 10+ a day, etc.

While the various steps in one embodiment of the method 2500 arepresented sequentially, one of ordinary skill will appreciate that someor all of the steps may be executed in different orders, may be combinedor omitted, and some or all of the steps may be executed in parallel.Further, in one or more of the example embodiments, one or more of thesteps shown in this example method may be omitted, repeated, and/orperformed in a different order. Furthermore, a person of ordinary skillin the art will appreciate that any equations utilized herein may bemodified without changing the meaning, for example, an equation may bemodified to use different units such as metric units without changingthe meaning. A person of ordinary skill in the art will appreciate thatadditional steps not shown in FIG. 25 may be included in performing thismethod. The method shown in FIG. 25 is merely one embodiment that can beperformed by using a system, such as described in FIG. 36 and FIG. 24 .FIGS. 1D-3, 24, and 36 are utilized in the discussion of FIG. 25 forease of understanding.

Referring to FIG. 25 , the method 2500 includes step 2505 to obtain(e.g., from the non-transitory storage medium such as the electronicstorage 3622) a tracer concentration history for each unique particulatetracer in produced fluid samples from a wellbore drilled into asubterranean formation. At least one unique particulate tracer is pumpedthroughout each stage, each stage group, or any combination thereofduring a hydraulic fracturing operation performed in the subterraneanformation. Each unique particulate tracer corresponds to an oil phase, awater phase, or a gas phase. For example, if a flow profile for the oilphase is desired, then unique oil particulate tracers that will react tooil should be pumped throughout the stages. If a flow profile for thewater phase is desired, then water unique particulate tracers that willreact to water should be pumped throughout the stages. If a flow profilefor the gas phase is desired, then gas unique particulate tracers thatwill react to gas should be pumped throughout the stages. The producedfluid samples comprise at least a portion of the unique particulatetracers that are pumped throughout the stages, the stage groups, or anycombination thereof.

The tracer concentration history of a specific unique particulate tracermay include a tracer concentration (e.g., in parts per billion (ppb)) asa function of time for the specific stage that it is pumped into duringthe hydraulic fracturing operation. The tracer concentration history foreach unique particulate tracer that is obtained at the step 2505 may bepreviously generated using laboratory analysis (discussed in FIG. 27 ).For example, the produced fluid samples obtained from the produced fluidfrom the wellbore may be analyzed in a laboratory using equipment and/ortests such as, but not limited to: chromatography.ultra-high-performance liquid chromatography (UHPLC) with a fluorescentlight scattering detector and a diode array detector (DAD) may be usedto obtain the spectral profile of samples, triple quad mass spec liquidchromatography may be used to integrate target ions and precursor ionsof the chemical of interest, or other known techniques to generate atracer concentration history for each unique particulate tracer. Thisgenerated tracer concentration history for each unique particulatetracer may be obtained from a non-transitory storage medium at the step2505. Two example tracer concentration histories in curve form areillustrated in FIG. 1H. The step 2505 may be performed using the tracerconcentration history component 2404.

Turning to the running example, the running example based on FIG. 1D-3assumes that the wellbore 120 produces oil, water, and gas, andtherefore, a unique oil particulate tracer, a unique water particulatetracer, and a unique gas particulate tracer are pumped throughout eachstage of the figure (i.e., throughout the nine stages). In other words,a total of twenty-seven unique particulate tracers (i.e., nine uniqueoil particulate tracers, nine unique water particulate tracers, and nineunique gas particulate tracers) are pumped in FIG. 1D-3 For simplicity,this running example assumes that all twenty-seven unique particulatetracers 170 a _(oil), 170 a _(water), 170 a _(gas), 170 b _(oil), 170 b_(water), 170 b _(gas), 170 c _(oil), 170 c _(water), 170 c _(gas), 170d _(oil), 170 d _(water), 170 d _(gas), 170 e _(oil), 170 e _(water),170 e _(gas), 170 f _(oil), 170 f _(water), 170 f _(gas), 170 g _(oil),170 g _(water), 170 g _(gas), 170 n-1 _(oil), 170 n-1 _(water), 170 n-1_(gas), 170 n _(oil), 170 n _(water), and 170 n _(gas) were detected bylaboratory analysis in the produced fluid samples from the wellbore 120.At step 2505, a tracer concentration history is obtained from anon-transitory storage medium for each of the twenty-seven uniqueparticulate tracers (i.e., twenty-seven tracer concentration historiesmay be obtained from the non-transitory storage medium).

The method 2500 includes step 2510 to obtain (e.g., from thenon-transitory storage medium such as the electronic storage 2422) aproduction history for the wellbore. The production history accounts forthe phases of the produced fluid of the wellbore, including the oilphase, the water phase, the gas phase, or any combination thereof. Theproduction history that is obtained may include quantity (e.g., barrels(bbls) per day) of oil that is produced from the wellbore, quantity(e.g., barrels (bbls) per day) of water that is produced from thewellbore, quantity (e.g., standard cubic feet (scf) per day) of gas thatis produced from the wellbore, or any combination thereof. For example,if the wellbore produces all three phases, then the production historyaccounts for all three phases. However, if the wellbore does not producegas, for example, then the production history may reflect water, oil, orboth water and oil but not gas.

In one embodiment, the production history may include quantity or rateof oil that is produced from the wellbore, quantity or rate of waterthat is produced from the wellbore, quantity or rate of gas that isproduced from the wellbore, or any combination thereof, for example, asa function of time. In one embodiment, the production history mayinclude additional information, such as, but not limited to, wellboreidentification information, well geographic properties (e.g., xcoordinate for the heel, y coordinate for the heel, depth, and/orazimuth), geologic properties (e.g., identification information for thesubterranean formation), wellbore properties (e.g., tortuosity),completion properties (e.g., perforated length, proppant intensity,and/or fracturing fluid intensity), etc. The production history for thewellbore that is obtained from the non-transitory storage medium at thestep 2510 may be previously generated using known techniques (discussedin FIG. 27 ). The step 2510 may be performed using the productionhistory component 2406.

The running example based on FIG. 1D-3 assumes that the wellbore 120produces oil, water, and gas. At step 2510, a production history may beobtained for the wellbore 120 that includes the quantity or rate of oilthat is produced from the wellbore 120, the quantity or rate of waterthat is produced from the wellbore 120, and the quantity or rate of gasthat is produced from the wellbore 120.

The method 2500 includes step 2515 to determine (e.g., with a physicalcomputer processor such as the processor 3618) a mean residence time foreach unique particulate tracer using the corresponding tracerconcentration history. For example, the mean residence time of aspecific unique particulate tracer generally refers to how quickly thatspecific unique particulate tracer gets produced from the stage that itis pumped into. How quickly a unique particulate tracer could getproduced is a function of the flowrate, and flowrate is defined asvolume over time (e.g., the contact volume proxy discussed hereinbelowover mean residence time). One diagram regarding mean residence time isillustrated in FIG. 26A.

In one embodiment, the mean residence time is determined using anequation as follows:

$t_{res} = \frac{\int_{t = 0}^{t = \infty}{c*t*{dt}}}{\int_{t = 0}^{t = \infty}{c*{dt}}}$

wherein t_(res) is mean residence time, c is tracer concentrationhistory, t is time, and dt is integration with respect to time.Additionally, t=0 is time starting from zero and t=∞ goes to infinity,thus, the time t can start at zero and go to a desired value up toinfinity. The unit for mean residence time may be in hours. The meanresidence time can be thought of as a time proxy over which the contactvolume proxy discussed hereinbelow gets produced. The mean residencetime equation hereinabove may be repeated for each unique particulatetracer using the corresponding tracer concentration history that wasobtained. The step 2515 may be performed using the mean residence timecomponent 2408.

In the running example based on FIG. 1D-3 , at step 2515, a meanresidence time may be determined using the equation above for each ofthe twenty-seven unique particulate tracers (i.e., twenty-seven meanresidence times may be determined).

The method 2500 includes step 2520 to determine (e.g., with the physicalcomputer processor such as the processor 3618) a contact volume proxyfor each unique particulate tracer using the production history and thecorresponding tracer concentration history. For example, the contactvolume proxy of a specific unique particulate tracer generally refers toan approximate volume of the subterranean formation that was contactedby the specific unique particulate tracer as itdiffused/leached/dissolved in the subterranean formation, or in otherwords, what is the approximate volume of the subterranean formationcontacted by the tracer cloud of the specific unique particulate tracer(discussed in FIG. 27 ). One diagram regarding contact volume proxy inthe subterranean formation 110 is illustrated in FIG. 26B. The proxy forvolume through which the tracer cloud flows (i.e., contact volume proxy)is illustrated as the area under the curves in FIG. 26A.

In one embodiment, the contact volume proxy is determined using anequation as follows:

vol_(proxy)=∫_(t=0) ^(t=∞) q*c*dt

Wherein vol_(proxy) is contact volume proxy, q is production history, cis tracer concentration history, t is time, and dt is integration withrespect to time. Additionally, t=0 is time starting from zero and t=∞goes to infinity, thus, the time t can start at zero and go to a desiredvalue up to infinity. The unit for contact volume proxy may be barrels(bbls). The contact volume proxy equation hereinabove may be repeatedfor each unique particulate tracer using the production history and thecorresponding tracer concentration history that were obtained. The step2520 may be performed using the contact volume proxy component 2410.

In the running example based on FIG. 1D-3 , at step 2520, a contactvolume proxy may be determined using the equation above for each of thetwenty-seven unique particulate tracers (i.e., twenty-seven contactvolume proxies may be determined).

The method 2500 includes step 2525 to determine (e.g., with the physicalcomputer processor such as the processor 3618) a flow profile for thewellbore for each phase indicative of flow contribution of each stage,each stage group, or any combination thereof by using the correspondingmean residence times and the corresponding contact volume proxies. Theflow contribution for each stage or stage group is determined, and then,the flow contributions corresponding to a specific phase are included ina flow profile for that specific phase (e.g., a flow profile for the oilphase, a separate flow profile for the water phase, and/or a separateflow profile for the gas phase). Each flow profile provides aquantitative evaluation of each stage or stage group's contribution toflow (e.g., per phase) that is not generally available for uniqueparticulate tracers that are placed throughout the entirety of stagesand/or stage groups. Each flow profile provides a quantitativeevaluation of each stage and/or stage group's contribution to flow thatis an improvement over the simple binary information of existingtechniques.

In one embodiment, the flow profile is determined using an equation asfollows:

${{flow\_ contribution}_{N}(\%)} = {\frac{\frac{{vol}_{{proxy}\_ N}}{t_{{res}\_ N}}}{\sum_{i = 1}^{i = M}\frac{{vol}_{{proxy}\_ i}}{t_{{res}\_ i}}}*100}$

wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, t_(res) is mean residence time, vol_(proxy) iscontact volume proxy, i is a counter, M is total number of stages orstage groups in which unique particulate tracers are pumped, and N isspecific stage or specific stage group for which flow contribution isdetermined. The flow contribution may be in the form of a percentage.The flow contribution equation hereinabove may be repeated for eachstage or stage group using the corresponding mean residence times andthe corresponding contact volume proxies that were determined.

A flow profile for a phase may include all the corresponding flowcontribution percentages determined with the equation hereinabove. Forexample, a flow profile for the oil phase includes all the flowcontribution percentages determined with the equation hereinabovecorresponding to the unique oil particulate tracers, which should sum upto about 100%. A separate flow profile for the water phase includes allthe flow contribution percentages determined with the equationhereinabove corresponding to the unique water particulate tracers, whichshould sum up to about 100%. A separate flow profile for the gas phaseincludes all the flow contribution percentages determined with theequation hereinabove corresponding to the unique gas particulatetracers, which should sum up to about 100%. A representation of eachflow profile for each phase may be generated and displayed using a barchart, line graph, curves, etc. using conventional techniques asdiscussed hereinbelow at step 2530. In one embodiment, a representationof a flow profile in terms of cumulative information (e.g., percentagecum oil along the lateral) may be generated and displayed. The step 2525may be performed using the flow profile component 2412.

In the running example based on FIG. 1D-3 , at step 2525, a flowcontribution may be determined using the equation above for each of thetwenty-seven unique particulate tracers (i.e., twenty-seven flowcontributions may be determined). A flow profile for the oil phase, forexample, in the form of a bar chart may be made using the nine flowcontribution percentages corresponding to the oil phase. A flow profilefor the water phase, for example, in the form of a bar chart may be madeusing the nine flow contribution percentages corresponding to the waterphase. A flow profile for the gas phase, for example, in the form of abar chart may be made using the nine flow contribution percentagescorresponding to the gas phase.

The method 2500 includes step 2530 to generate, on a graphical userinterface such as the graphical display 3624, a representation of theflow profile for the wellbore for each phase indicative of the flowcontribution of each stage, each stage group, or any combinationthereof, and display, via the graphical user interface, therepresentation. Visual effects may be utilized to illustrate flowcontribution per stage and/or stage group in the flow profile. Arepresentation of each flow profile for each phase may be generated anddisplayed using a bar chart, line graph, curves, etc. The representationof each flow profile for each phase may include confidence levels, flowcontribution information determined in another manner (e.g., usinglogging equipment, sensors, or other equipment) for comparison, etc. Inone embodiment, a representation of a flow profile in terms ofcumulative information (e.g., percentage cum oil along the lateral) maybe generated and displayed. Examples of flow profiles for an oil phaseare illustrated in FIGS. 33A-33H.

In the running example based on FIG. 1D-3 , at step 2530, threerepresentations of flow profiles may be generated and displayed (e.g., arepresentation of the flow profile for the oil phase in the form of abar chart using the nine flow contribution percentages corresponding tothe oil phase, a representation of the flow profile for the water phasein the form of a bar chart using the nine flow contribution percentagescorresponding to the water phase, and a representation of the flowprofile for the gas phase in the form of a bar chart using the nine flowcontribution percentages corresponding to the gas phase).

Those of ordinary skill in the art will appreciate that variousmodifications may be made to the description above. As an example, FIG.1D-3 illustrates individual stages instead of stage groups forsimplicity, however, a person of ordinary skill in the art willappreciate that the steps 2505-2530 are also applicable in the contextof one or more stage groups. As another example, the method 2500 mayinclude an optional step 2535 to smooth a tracer concentration historyfor a specific unique particulate tracer before c) of step 2515 and d)of step 2520 to reduce noise (e.g., reduce points that show largevariations ups and/or downs); and utilize the smoothed tracerconcentration history for the specific unique particulate tracer in c)of step 2515 and d) of step 2520. This optional step 2535 may beperformed by curve fitting to smoothen out the data (e.g., normal, lognormal, or other representative curve fit). As another example, a personof ordinary skill in the art will appreciate that a single phase likethe oil phase may be of interest so unique oil particulate tracers onlymay be pumped throughout the stages and/or stage groups (or two phasesmay be of interest and those corresponding unique particulate tracersmay be pumped throughout the stages and/or stage groups). Thus, themethod 2500 applies to one phase, two phases, or three phases. Asanother example, the method 2500 may be used for laterals, verticalwellbores, etc.

FIG. 27 illustrates an example method 2700 for determining a flowprofile for a wellbore using unique particulate tracers. The method 2700of FIG. 27 may include at least one of the steps of the method 2500 ofFIG. 25 . The method 2700 may also be referred to as a response timedelay method herein (e.g., Response time delay, rate=volume/time),however, those of ordinary skill in the art will appreciate that thisterminology is not meant to be limiting. The method 2700 may be utilizedif high frequency data with mode is accurately captured with time (e.g.,high frequency sampling depending on the flow rate) and/or low oil rate.For example, the response delay method may be applied when data iscollected in the first 5 days after POP (i.e., popping the wellbore openafter shut-in period), such as collecting produced fluid samples atleast once a day to about 5+a day, at least once a day to about 10+aday, etc. The discussion of method 2700 of FIG. 27 will focus onphysical steps that may be performed at the wellbore, in the field,and/or at a laboratory before the method 2500 of FIG. 25 , as generallyillustrated in FIG. 24 .

While the various steps in one embodiment of the method 2700 arepresented sequentially, one of ordinary skill will appreciate that someor all of the steps may be executed in different orders, may be combinedor omitted, and some or all of the steps may be executed in parallel.Further, in one or more of the example embodiments, one or more of thesteps shown in this example method may be omitted, repeated, and/orperformed in a different order. Furthermore, a person of ordinary skillin the art will appreciate that any equations utilized herein may bemodified without changing the meaning, for example, an equation may bemodified to use different units such as metric units without changingthe meaning. A person of ordinary skill in the art will appreciate thatadditional steps not shown in FIG. 27 may be included in performing thismethod. The method shown in FIG. 27 is merely one embodiment that can beperformed by using a system, such as described in FIG. 36 and FIG. 24 .FIGS. 1D-3, 24, and 36 are utilized in the discussion of FIG. 27 forease of understanding.

Referring to FIG. 27 , the method 2700 includes step 2705 to pump atleast one unique particulate tracer throughout each stage, each stagegroup, or any combination thereof during a hydraulic fracturingoperation performed in the subterranean formation, such as in FIG. 1D-3. Each unique particulate tracer corresponds to an oil phase, a waterphase, or a gas phase. For example, the unique particulate tracers maybe blended with proppant (e.g., sand) (e.g., the proppant 112) andpumped throughout stages, stage groups, or any combination thereof. Asanother example, the unique particulate tracers may be directly injectedinto the fracturing fluid stream and pumped throughout stages, stagegroups, or any combination thereof. Practically any pumping equipment orpumping technique known in the art for pumping unique particulatetracers throughout stages, stage groups, or any combination thereof maybe utilized.

In the running example based on FIG. 1D-3 , at step 2705, the proppant112 and the twenty-seven unique particulate tracers 170 a _(oil), 170 a_(water), 170 a _(gas), 170 b _(oil), 170 b _(water), 170 b _(gas), 170c _(oil), 170 c _(water), 170 c _(gas), 170 d _(oil), 170 d _(water),170 d _(gas), 170 e _(oil), 170 e _(water), 170 e _(gas), 170 f _(oil),170 f _(water), 170 f _(gas), 170 g _(oil), 170 g _(water), 170 g_(gas), 170 n-1 _(oil), 170 n-1 _(water), 170 n-1 _(gas), 170 n _(oil),170 n _(water), and 170 n _(gas) are pumped into the nine stages asillustrated in FIG. 24 .

The method 2700 includes step 2710 to shut-in the wellbore for a periodof time to cause tracer clouds to form in the subterranean formation forat least a portion of the unique particulate tracers that are pumpedthroughout the stages, the stage groups, or any combination thereof.Shutting in of the wellbore may help build the tracer cloud for eachunique particulate tracer pumped as it diffuses/leaches/dissolves in thesubterranean formation. The wellbore is shut-in for a period of timethat is long enough for the injected unique particulate tracers to bedetected in the produced fluid samples. The wellbore may be shut-in fora period of time such as 1 day to 3 days (i.e., 24 hours to 72 hours).The longer the wellbore has been producing, then the longer the shut-inperiod in some embodiments, such as a shut-in period of upto 5 days(i.e., upto 120 hours). The period of time for the shut-in may depend onthe unique particulate tracers pumped, logistics and practical realitiesassociated with shutting in a wellbore, etc. The wellbore may be shut-inusing known techniques for shutting in wellbores. In short, the step2710 shut-in the wellbore for enough time for tracer clouds to bedeveloped so detectable tracer concentrations are produced. FIGS.28A-28B illustrate an example of shut-in to build up tracer clouds.

In the running example based on FIG. 1D-3 , at step 2710, the wellbore120 is shut-in for a period of time long enough for tracer clouds to bedeveloped for the twenty-seven unique particulate tracers 170 a _(oil),170 a _(water), 170 a _(gas), 170 b _(oil), 170 b _(water), 170 b_(gas), 170 c _(oil), 170 c _(water), 170 c _(gas), 170 d _(oil), 170 d_(water), 170 d _(gas), 170 e _(oil), 170 e _(water), 170 e _(gas), 170f _(oil), 170 f _(water), 170 f _(gas), 170 g _(oil), 170 g _(water),170 g _(gas), 170 n-1 _(oil), 170 n-1 _(water), 170 n-1 _(gas), 170 n_(oil), 170 n _(water), and 170 n _(gas) so detectable tracerconcentrations are produced from the wellbore 120 as illustrated in FIG.24 . For example, the wellbore 120 may be shut-in long enough to developthe twenty-seven tracer clouds for the twenty-seven unique particulatetracers.

The method 2700 includes step 2715 to flow back the wellbore to causeproduced fluid from the wellbore after the shut-in period. For example,the wellbore flows back up for the time in which the tracer clouds areproduced back (e.g., typically 5 to 7 days). The produced fluid samplescomprise at least a portion of the unique particulate tracers that arepumped throughout the stages, the stage groups, or any combinationthereof.

In the running example based on FIG. 1D-3 , at step 2715, the wellbore120 is flowed back to cause produced fluid to exit the wellbore 120.

The method 2700 includes step 2720 to obtain produced fluid samplescomprising unique particulate tracers from a wellbore drilled into asubterranean formation. One embodiment may include sampling frequentlyfor the first few days (˜5 days and a function of flow rate) until thetracer clouds get produced. The samples from the produced fluid may beobtained directly from a wellhead that is fluidly coupled to thewellbore using practically any technique and/or equipment known in theart for sampling produced fluid. Information about an automated tracersampling and measurement system may be found in U.S. Patent PublicationApplication No. 2014/0260694, which is incorporated by reference.

In the running example based on FIG. 1D-3 , at step 2720, produced fluidsamples may be collected from the wellbore 120, such as from thewellhead of the wellbore 120. The produced fluid samples comprise atleast a portion of the twenty-seven unique particulate tracers that arepumped throughout the nine stages. For example, produced fluid samplesmay be collected at least once a day to about 5+ a day, at least once aday to about 10+ a day, etc. for approximately five days.

The method 2700 includes step 2725 to analyze the produced fluid samplesobtained from the produced fluid to generate the tracer concentrationhistory for each unique particulate tracer. For example, the producedfluid samples obtained from the produced fluid from the wellbore may beanalyzed in a laboratory using equipment and/or tests such as, but notlimited to: chromatography, ultra-high-performance liquid chromatography(UHPLC) with a fluorescent light scattering detector and a diode arraydetector (DAD) may be used to obtain the spectral profile of samples,triple quad mass spec liquid chromatography may be used to integratetarget ions and precursor ions of the chemical of interest, or otherknown techniques to generate a tracer concentration history for eachunique particulate tracer. The generated tracer concentration historiesmay be provided to the system 3600 (e.g., one or more remote computingdevices of the laboratory may be communicatively coupled to the system3600 via a wired or wireless connection). The generated tracerconcentration history for each unique particulate tracer may be obtainedfrom a non-transitory storage medium at the step 2505 and used todetermine a flow profile for each phase as described hereinabove inconnection with FIGS. 24, 25, and 36 .

In the running example based on FIG. 1D-3 , at step 2725, twenty-seventracer concentration histories may be generated in the laboratory andused to determine a flow profile for each phase.

The method 2700 includes step 2730 to determine the production historyof the wellbore. Practically any technique and/or equipment (e.g.,downhole and/or on the surface) such as flow meters, temperaturesensors, pressure pressures, separators (e.g., using a test separator inthe field for about 24 hours), etc. may be utilized to generate theproduction history. The production history may be determined in thefield using this equipment. Information about generating a productionhistory is provided at the following: Izgec, B., Hasan, A. R. R., Lin,D, and C. S. S. Kabir. “Flow-Rate Estimation From Wellhead-Pressure andTemperature Data.” SPE Prod & Oper 25 (2010): 31-39, which isincorporated by reference. The generated production history of thewellbore may be provided to the system 3600 (e.g., one or more remotemeters, remote sensors, or computing devices may be communicativelycoupled to the system 3600 via a wired or wireless connection). Thegenerated production history for the wellbore may be obtained from anon-transitory storage medium at the step 2510 and used to determine aflow profile for each phase as described hereinabove in connection withFIGS. 24, 25, and 36 .

In the running example based on FIG. 1D-3 , at step 2730, a productionhistory may be generated for the wellbore 120 and used to determine aflow profile for each phase.

The method 2700 includes a step of determining a flow profile for thewellbore for each phase using the produced fluid samples comprising theunique particulate tracers by: a) obtaining a tracer concentrationhistory for each unique particulate tracer; b) obtaining a productionhistory for the wellbore; c) determining a mean residence time for eachunique particulate tracer using the corresponding tracer concentrationhistory; d) determining a contact volume proxy for each uniqueparticulate tracer using the production history and the correspondingtracer concentration history; and e) determining the flow profile forthe wellbore for each phase indicative of flow contribution of eachstage, each stage group, or any combination thereof by using thecorresponding mean residence times and the corresponding contact volumeproxies. In one embodiment, the step may be performed as explainedhereinabove in connection with FIGS. 24, 25, and 36 . However, the step2735 may be performed in other ways in some embodiments. In oneembodiment, one or more of the steps of the method 2700 may beimplemented using a computing system such as in FIG. 36 .

Decline Method:

The methods and systems of the present disclosure may be implemented bya system and/or in a system, such as a system 3600 shown in FIG. 36 andFIG. 29 . A method of determining a flow profile for a wellbore usingunique particulate tracers may be performed by the processor 3618,including input such as at least one tracer concentration history (e.g.,a tracer concentration history for each unique particulate tracer)and/or optionally a production history for a wellbore as well as outputsuch as a flow profile for the wellbore for each phase indicative offlow contribution of each stage, each stage group, or any combinationthereof. The electronic storage 3622 may store information relating tothe tracer concentration history for each unique particulate tracer,optionally the production history of the wellbore, information about theproduced fluid samples, and/or other information. The graphical display3624 may present information relating to the flow profile for thewellbore for each phase indicative of the flow contribution of eachstage, each stage group, or any combination thereof, and/or otherinformation.

The processor 3618 may be configured to execute one or moremachine-readable instructions 3602 to facilitate determining the flowprofile for the wellbore for each phase using the particulate tracers.The machine-readable instructions 3602 may include one or more computerprogram components. The machine-readable instructions 3602 may include atracer concentration history component 2904, optionally a productionhistory component 2906, a decline rate component 2908, a normalizationfactor component 2910, a normalized decline rate component 2911, a flowprofile component 2912, a smoothing component 2914, a representationcomponent 2916, and/or other computer program components.

The tracer concentration history component 2904 may be configured toobtain (e.g., from the non-transitory storage medium such as theelectronic storage 3622) a tracer concentration history for each uniqueparticulate tracer in produced fluid samples from a wellbore drilledinto a subterranean formation. At least one unique particulate tracer ispumped throughout each stage, each stage group, or any combinationthereof during a hydraulic fracturing operation performed in thesubterranean formation. Each unique particulate tracer corresponds to anoil phase, a water phase, or a gas phase. The produced fluid samplescomprise at least a portion of the unique particulate tracers that arepumped throughout the stages, the stage groups, or any combinationthereof.

The optional production history component 2906 may be configured toobtain (e.g., from the non-transitory storage medium such as theelectronic storage 3622) a production history for the wellbore.

The decline rate component 2908 may be configured to determine (e.g.,with the physical computer processor such as the processor 3618) adecline rate for each unique particulate tracer using the correspondingtracer concentration history.

The normalization factor component 2910 may be configured to determine(e.g., with the physical computer processor such as the processor 3618)a normalization factor for each unique particulate tracer using thecorresponding tracer concentration history and optionally the productionhistory.

The normalized decline rate component 2911 may be configured todetermine (e.g., with the physical computer processor such as theprocessor 3618) a normalized decline rate for each unique particulatetracer using the corresponding decline rate and the correspondingnormalization factor.

The flow profile component 2912 may be configured to determine (e.g.,with the physical computer processor such as the processor 3618) a flowprofile for the wellbore for each phase indicative of flow contributionof each stage, each stage group, or any combination thereof by using thecorresponding normalized decline rates.

The smoothing component 2914 may be configured to smooth (e.g., with thephysical computer processor such as the processor 3618) a tracerconcentration history for a specific unique particulate tracer beforedetermining a decline rate and before determining a normalization factorto reduce noise. The smoothed tracer concentration history for thespecific unique particulate tracer may be utilized in determining thedecline rate and determining the normalization factor.

The representation component 2916 may be configured to generate (e.g.,on the graphical user interface such as the graphical display 3624) arepresentation of the flow profile for the wellbore for each phaseindicative of the flow contribution of each stage, each stage group, orany combination thereof. The representation component 2916 may beconfigured to display (e.g., on the graphical user interface such as thegraphical display 3624) the representation.

FIG. 30 illustrates an example method 3000 for determining a flowprofile for a wellbore using unique particulate tracers. The method 3000may be referred to as a decline method herein, however, those ofordinary skill in the art will appreciate that this terminology is notmeant to be limiting. The method 3000 may be utilized to determine aflow profile for a wellbore per phase during producing life if highfrequency data is not available and/or high oil rate (e.g., a high oilrate may be about 1,000 bbls a day). The method 3000 may be utilized todetermine a flow profile for a wellbore per phase if tracer leach rate(diffusion) is not known.

While the various steps in one embodiment of the method 3000 arepresented sequentially, one of ordinary skill will appreciate that someor all of the steps may be executed in different orders, may be combinedor omitted, and some or all of the steps may be executed in parallel.Further, in one or more of the example embodiments, one or more of thesteps shown in this example method may be omitted, repeated, and/orperformed in a different order. Furthermore, a person of ordinary skillin the art will appreciate that any equations utilized herein may bemodified without changing the meaning, for example, an equation may bemodified to use different units such as metric units without changingthe meaning. A person of ordinary skill in the art will appreciate thatadditional steps not shown in FIG. 30 may be included in performing thismethod. The method shown in FIG. 30 is merely one embodiment that can beperformed by using a system, such as described in FIG. 36 and FIG. 29 .FIGS. 1D-3, 29, and 36 are utilized in the discussion of FIG. 30 forease of understanding.

Referring to FIG. 30 , the method 3000 includes step 3005 to obtain(e.g., from the non-transitory storage medium such as the electronicstorage 3622) a tracer concentration history for each unique particulatetracer in produced fluid samples from a wellbore drilled into asubterranean formation. At least one unique particulate tracer is pumpedthroughout each stage, each stage group, or any combination thereofduring a hydraulic fracturing operation performed in the subterraneanformation. Each unique particulate tracer corresponds to an oil phase, awater phase, or a gas phase. For example, if a flow profile for the oilphase is desired, then unique oil particulate tracers that will react tooil should be pumped throughout the stages. If a flow profile for thewater phase is desired, then water unique particulate tracers that willreact to water should be pumped throughout the stages. If a flow profilefor the gas phase is desired, then gas unique particulate tracers thatwill react to gas should be pumped throughout the stages. The producedfluid samples comprise at least a portion of the unique particulatetracers that are pumped throughout the stages, the stage groups, or anycombination thereof.

The tracer concentration history of a specific unique particulate tracermay include a tracer concentration (e.g., in parts per billion (ppb)) asa function of time for the specific stage that it is pumped into duringthe hydraulic fracturing operation. The tracer concentration history foreach unique particulate tracer that is obtained at the step 3005 may bepreviously generated using laboratory analysis (discussed in FIG. 27 ).For example, the produced fluid samples obtained from the produced fluidfrom the wellbore may be analyzed in a laboratory using equipment and/ortests such as, but not limited to: chromatography.ultra-high-performance liquid chromatography (UHPLC) with a fluorescentlight scattering detector and a diode array detector (DAD) may be usedto obtain the spectral profile of samples, triple quad mass spec liquidchromatography may be used to integrate target ions and precursor ionsof the chemical of interest, or other known techniques to generate atracer concentration history for each unique particulate tracer. Thisgenerated tracer concentration history for each unique particulatetracer may be obtained from a non-transitory storage medium at the step3005. Two example tracer concentration histories in curve form areillustrated in FIG. 1H. The step 3005 may be performed using the tracerconcentration history component 2904.

Turning to the running example, the running example based on FIG. 1D-3assumes that the wellbore 120 produces oil, water, and gas, andtherefore, a unique oil particulate tracer, a unique water particulatetracer, and a unique gas particulate tracer are pumped throughout eachstage of the figure (i.e., throughout the nine stages). In other words,a total of twenty-seven unique particulate tracers (i.e., nine uniqueoil particulate tracers, nine unique water particulate tracers, and nineunique gas particulate tracers) are pumped in FIG. 1D-3 For simplicity,this running example assumes that all twenty-seven unique particulatetracers 170 a _(oil), 170 a _(water), 170 a _(gas), 170 b _(oil), 170 b_(water), 170 b _(gas), 170 c _(oil), 170 c _(water), 170 c _(gas), 170d _(oil), 170 d _(water), 170 d _(gas), 170 e _(oil), 170 e _(water),170 e _(gas), 170 f _(oil), 170 f _(water), 170 f _(gas), 170 g _(oil),170 g _(water), 170 g _(gas), 170 n-1 _(oil), 170 n-1 _(water), 170 n-1_(gas), 170 n _(oil), 170 n _(water), and 170 n _(gas) were detected bylaboratory analysis in the produced fluid samples from the wellbore 120.At step 3005, a tracer concentration history is obtained from anon-transitory storage medium for each of the twenty-seven uniqueparticulate tracers (i.e., twenty-seven tracer concentration historiesmay be obtained from the non-transitory storage medium).

The method 3000 includes optional step 3010 to obtain (e.g., from thenon-transitory storage medium such as the electronic storage 3622) aproduction history for the wellbore. The production history accounts forthe phases of the produced fluid of the wellbore, including the oilphase, the water phase, the gas phase, or any combination thereof. Theproduction history that is obtained may include quantity (e.g., barrels(bbls) per day) of oil that is produced from the wellbore, quantity(e.g., barrels (bbls) per day) of water that is produced from thewellbore, quantity (e.g., standard cubic feet (scf) per day) of gas thatis produced from the wellbore, or any combination thereof. For example,if the wellbore produces all three phases, then the production historyaccounts for all three phases. However, if the wellbore does not producegas, for example, then the production history may reflect water, oil, orboth water and oil but not gas.

In one embodiment, the production history may include quantity or rateof oil that is produced from the wellbore, quantity or rate of waterthat is produced from the wellbore, quantity or rate of gas that isproduced from the wellbore, or any combination thereof, for example, asa function of time. In one embodiment, the production history mayinclude additional information, such as, but not limited to, wellboreidentification information, well geographic properties (e.g., xcoordinate for the heel, y coordinate for the heel, depth, and/orazimuth), geologic properties (e.g., identification information for thesubterranean formation), wellbore properties (e.g., tortuosity),completion properties (e.g., perforated length, proppant intensity,and/or fracturing fluid intensity), etc. The production history for thewellbore that is obtained from the non-transitory storage medium at thestep 3010 may be previously generated using known techniques (discussedin FIG. 27 ). The step 3010 may be performed using the productionhistory component 2906.

The running example based on FIG. 1D-3 assumes that the wellbore 120produces oil, water, and gas. At step 3010, a production history may beobtained for the wellbore 120 that includes the quantity or rate of oilthat is produced from the wellbore 120, the quantity or rate of waterthat is produced from the wellbore 120, and the quantity or rate of gasthat is produced from the wellbore 120.

The method 3000 includes step 3015 to determine (e.g., with a physicalcomputer processor such as the processor 3618) a decline rate for eachunique particulate tracer using the corresponding tracer concentrationhistory. For example, flow rate from the stages and/or stage groups is afunction of how quickly the tail of a tracer concentration history curvedeclines from a stage and/or stage group. The faster the decline, thehigher the flow rate because the tracer cloud would be produced quickerand vice versa. Two diagrams regarding decline rate are illustrated inFIGS. 31A-31B.

In one embodiment, the decline rate is determined using an equation asfollows:

$r = \frac{dc}{dt}$

wherein r is decline rate, dC is integration with respect to tracerconcentration history, and dt is integration with respect to time. Thedecline rate is the slope of a tail for a tracer concentration historycurve as shown in the plot to the right as r1 and r2 in FIG. 31B. Theunit for decline rate may be in parts per billion (ppb) per day. Thetail of a specific tracer concentration history is where the slopebecomes substantially constant (and stops changing). The decline rateequation hereinabove may be repeated for each unique particulate tracerusing the corresponding tracer concentration history that was obtained.The step 3015 may be performed using the mean residence time component2908.

In the running example based on FIG. 1D-3 , at step 3015, a decline ratemay be determined using the equation above for each of the twenty-sevenunique particulate tracers (i.e., twenty-seven decline rates may bedetermined).

The method 3000 includes step 3020 to determine (e.g., with the physicalcomputer processor such as the processor 3618) a normalization factorfor each unique particulate tracer using the corresponding tracerconcentration history and optionally the production history. Each tracercloud has a different amount of particulate tracer in it so the method3000 normalizes the concentration so that the decline rates define theflow rate properly. A normalization factor may be utilized for thenormalization, and the normalization factor may be determined in twoways. Normalizing with the maximum/peak value of the concentration orthe area under the curve are appropriate normalization factors.

In one embodiment, a first normalization factor is represented as:norm_(factor) =c _(mode) wherein norm_factor is normalization factor andc_(mode) is a maximum value of a tracer concentration history (e.g.,maximum value of a tracer concentration history curve). The unit fornormalization factor may be in parts per billion (ppb). Thenormalization factor equation hereinabove may be repeated for eachunique particulate tracer using the corresponding tracer concentrationhistory that were obtained. The step 3020 may be performed using thenormalization factor component 2910.

In one embodiment, a second normalization factor is determined using anequation as follows:

norm_(factor)=∫_(t=0) ^(t=∞) q*ρ*c*dt

wherein norm_factor is normalization factor, t is time, q is productionhistory, ρ is fluid density (e.g., in pounds per feet), c is tracerconcentration history, and dt is integration with respect to time.Additionally, t=0 is time starting from zero and t=∞ goes to infinity,thus, the time t can start at zero and go to a desired value up toinfinity. The unit for the normalization factor may be in pounds. Thenormalization factor equation hereinabove may be repeated for eachunique particulate tracer using the corresponding tracer concentrationhistory and the production history that were obtained. The step 3020 maybe performed using the normalization factor component 2910.

In the running example based on FIG. 1D-3 , at step 3020, anormalization factor may be determined using one of the equations abovefor each of the twenty-seven unique particulate tracers (i.e.,twenty-seven normalization factors may be determined).

The method 3000 includes step 3025 to determine (e.g., with the physicalcomputer processor such as the processor 3618) a normalized decline ratefor each unique particulate tracer using the corresponding decline rateand the corresponding normalization factor. In one embodiment, thenormalized decline rate is determined using an equation as follows:

${r\_ norm} = \frac{r}{norm\_ factor}$

wherein r_norm is normalized decline rate, r is decline rate, andnorm_factor is normalization factor. The unit for normalized declinerate may be in 1/pound if the second normalization factor is utilized.The normalized decline rate hereinabove may be repeated for each uniqueparticulate tracer using the corresponding decline rate and thecorresponding normalization factor that were obtained. The step 3025 maybe performed using the normalized decline rate component 2911.

In the running example based on FIG. 1D-3 , at step 3025, a normalizeddecline rate may be determined using the equation above for each of thetwenty-seven unique particulate tracers (i.e., twenty-seven normalizeddecline rates may be determined).

The method 3000 includes step 3030 to determine (e.g., with the physicalcomputer processor such as the processor 3618) a flow profile for thewellbore for each phase indicative of flow contribution of each stage,each stage group, or any combination thereof by using the correspondingnormalized decline rates. The flow contribution for each stage or stagegroup is determined, and then, the flow contributions corresponding to aspecific phase are included in a flow profile for that specific phase(e.g., a flow profile for the oil phase, a separate flow profile for thewater phase, and/or a separate flow profile for the gas phase). Eachflow profile provides a quantitative evaluation of each stage or stagegroup's contribution to flow (e.g., per phase) that is not generallyavailable for unique particulate tracers that are placed throughout theentirety of stages and/or stage groups. Each flow profile provides aquantitative evaluation of each stage and/or stage group's contributionto flow that is an improvement over the simple binary information ofexisting techniques.

In one embodiment, the flow profile is determined using an equation asfollows:

${{flow\_ contribution}_{N}(\%)} = {\frac{r_{{norm}\_ N}}{\sum_{I = 1}^{i = M}{r_{{norm} -}i}}*100}$

wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, r_(norm) is normalized decline rate, i is acounter, M is total number of stages or stage groups in which uniqueparticulate tracers are pumped, and N is specific stage or specificstage group for which flow contribution is determined. The flowcontribution may be in the form of a percentage. The flow contributionequation hereinabove may be repeated for each stage or stage group usingthe corresponding normalized decline rates that were determined.

A flow profile for a phase may include all the corresponding flowcontribution percentages determined with the equation hereinabove. Forexample, a flow profile for the oil phase includes all the flowcontribution percentages determined with the equation hereinabovecorresponding to the unique oil particulate tracers, which should sum upto about 100%. A separate flow profile for the water phase includes allthe flow contribution percentages determined with the equationhereinabove corresponding to the unique water particulate tracers, whichshould sum up to about 100%. A separate flow profile for the gas phaseincludes all the flow contribution percentages determined with theequation hereinabove corresponding to the unique gas particulatetracers, which should sum up to about 100%. A representation of eachflow profile for each phase may be generated and displayed using a barchart, line graph, curves, etc. using conventional techniques asdiscussed hereinbelow at step 3030. In one embodiment, a representationof a flow profile in terms of cumulative information (e.g., percentagecum oil along the lateral) may be generated and displayed. The step 3030may be performed using the flow profile component 2912.

In the running example based on FIG. 1D-3 , at step 3030, a flowcontribution may be determined using the equation above for each of thetwenty-seven unique particulate tracers (i.e., twenty-seven flowcontributions may be determined). A flow profile for the oil phase, forexample, in the form of a bar chart may be made using the nine flowcontribution percentages corresponding to the oil phase. A flow profilefor the water phase, for example, in the form of a bar chart may be madeusing the nine flow contribution percentages corresponding to the waterphase. A flow profile for the gas phase, for example, in the form of abar chart may be made using the nine flow contribution percentagescorresponding to the gas phase.

The method 3000 includes step 3035 to generate, on a graphical userinterface such as the graphical display 3624, a representation of theflow profile for the wellbore for each phase indicative of the flowcontribution of each stage, each stage group, or any combinationthereof, and display, via the graphical user interface, therepresentation. Visual effects may be utilized to illustrate flowcontribution per stage and/or stage group in the flow profile. Arepresentation of each flow profile for each phase may be generated anddisplayed using a bar chart, line graph, curves, etc. The representationof each flow profile for each phase may include confidence levels, flowcontribution information determined in another manner (e.g., usinglogging equipment, sensors, or other equipment) for comparison, etc. Inone embodiment, a representation of a flow profile in terms ofcumulative information (e.g., percentage cum oil along the lateral) maybe generated and displayed. Examples of flow profiles for an oil phaseare illustrated in FIGS. 33A-33H.

In the running example based on FIG. 1D-3 , at step 3035, threerepresentations of flow profiles may be generated and displayed (e.g., arepresentation of the flow profile for the oil phase in the form of abar chart using the nine flow contribution percentages corresponding tothe oil phase, a representation of the flow profile for the water phasein the form of a bar chart using the nine flow contribution percentagescorresponding to the water phase, and a representation of the flowprofile for the gas phase in the form of a bar chart using the nine flowcontribution percentages corresponding to the gas phase).

Those of ordinary skill in the art will appreciate that variousmodifications may be made to the description above. As an example, FIG.1D-3 illustrates individual stages instead of stage groups forsimplicity, however, a person of ordinary skill in the art willappreciate that the steps 3005-3035 are also applicable in the contextof one or more stage groups. As another example, the method 3000 mayinclude an optional step 3040 to smooth a tracer concentration historyfor a specific unique particulate tracer before c) of step 3015 and d)of step 3020 to reduce noise (e.g., reduce points that show largevariations ups and/or downs); and utilize the smoothed tracerconcentration history for the specific unique particulate tracer in c)of step 3015 and d) of step 3020. For example, the optional step 3040may smoothen out a tail of the tracer concentration history for aspecific unique particulate tracer. This optional step 3040 may beperformed by curve fitting to smoothen out the data (e.g., linearregression or other representative curve fit). As another example, aperson of ordinary skill in the art will appreciate that a single phaselike the oil phase may be of interest so unique oil particulate tracersonly may be pumped throughout the stages and/or stage groups (or twophases may be of interest and those corresponding unique particulatetracers may be pumped throughout the stages and/or stage groups). Thus,the method 2500 applies to one phase, two phases, or three phases. Asanother example, the method 3000 may be used for laterals, verticalwellbores, etc.

FIG. 32 illustrates an example method 3200 for determining a flowprofile for a wellbore using unique particulate tracers. The method 3200of FIG. 32 may include at least one of the steps of the method 3000 ofFIG. 30 . The method 3200 of FIG. 32 may include at least one of thesteps of the method 2700 of FIG. 27 and FIG. 29 . The method 3200 mayalso be referred to as a decline method herein, however, those ofordinary skill in the art will appreciate that this terminology is notmeant to be limiting. The method 3200 may be utilized to determine aflow profile for a wellbore per phase during producing life if highfrequency data is not available and/or high oil rate (e.g., a high oilrate may be about 1,000 bbls a day). The method 3200 may be utilized todetermine a flow profile for a wellbore per phase if tracer leach rate(diffusion) is not known.

While the various steps in one embodiment of the method 3200 arepresented sequentially, one of ordinary skill will appreciate that someor all of the steps may be executed in different orders, may be combinedor omitted, and some or all of the steps may be executed in parallel.Further, in one or more of the example embodiments, one or more of thesteps shown in this example method may be omitted, repeated, and/orperformed in a different order. Furthermore, a person of ordinary skillin the art will appreciate that any equations utilized herein may bemodified without changing the meaning, for example, an equation may bemodified to use different units such as metric units without changingthe meaning. A person of ordinary skill in the art will appreciate thatadditional steps not shown in FIG. 32 may be included in performing thismethod. The method shown in FIG. 32 is merely one embodiment that can beperformed by using a system, such as described in FIG. 36 and FIG. 29 .In one embodiment, one or more of the steps of the method 3200 may beimplemented using a computing system such as in FIG. 36 .

Response Time Delay Method and Decline Method Examples:

FIGS. 33A-33H illustrate various examples of flow profiles for an oilphase only (i.e., unique oil particulate tracers are pumped throughoutstage groups) and corresponding tracer concentrations histories for theexamples. Tracer concentration histories for time period A (Post POP) inFIG. 33D and for time period B in 33A are illustrated in the figures.Logging information for time period C was also obtained and utilized forcomparisons. In FIGS. 33B-33C and 33G-33H, tracer interpretation showsgood correspondence with the logging interpretation. In FIGS. 33D-33E,tracer interpretation post POP using the response time delay method forperiod A and using the delay method for period B also show change in theflow contribution from the toe stages in the 3 month production period,which allows for time-based flow profiling. The response time delaymethod and the decline method may be utilized on the substantially samedata as illustrated in FIGS. 33G-33H. FIGS. 34A-34B and 35A alsoillustrate tracer concentration histories used with the response timedelay method and the decline method as in FIGS. 34C and 35B,respectively.

A person of ordinary skill in the art will appreciate that tracer basedflow profiling may accomplish the following: (1) eliminate uncertaintydue to well trajectory, (2) uncertainty due to multi-phase flow issuesin the wellbore if the reservoir contact volume is larger than thewellbore volume, and/or (3) flow profiling as a function of time withminimal intervention (e.g., shutting in the well for 24 to 48 hours andhigh frequency sampling post shut-in). Of note, (a) tracer release rateunderstanding is important for correct interpretation post POP in theflowing life of the wellbore for response time delay method, but thedecline method is independent of the release rate as long as enoughtracer is detected, (b) flowback sampling frequency post shut-in shouldbe high when the oil flowrates increase for response time delay methodto work correctly, (c) lower resolution because of the limitation withthe number of tracers available, and/or (d) 24 hour LPO if flowprofiling is desired after initial POP but could be synchronized withplanned shut-ins/workovers. Of note, some considerations include (I)does not depend on the release rate explicitly but assumes that all theparticulate tracers have the same release rate as a function of time andwould enable flow profiling over time, (II) tracer baseline can bededuced from the tracer signal itself if the previous statement ontracer design is true, and/or (III) particulate tracers may providemeaningful signal over the early life (at least 1 year) of the well.Advantages include: (i) non-interventional flow profiling which could beused upto 12 months and extended to 18 months and/or (ii) test could beplanned when changes in well behavior are observed. Indeed, it isoftentimes difficult, expensive, or not practical to use logging toolsand generate logging data (e.g., especially in geographically remoteareas) so tracer-based flow profiling may provide adequate flowprofiles, even though tracer based flow profiling may produce lowerresolution data as compared to logging data.

Computer System:

The system 3600 may include one or more of a processor 3618, aninterface 3620 (e.g., bus, wireless interface), an electronic storage3622, a graphical display 3624, and/or other components. The electronicstorage 3622 may be configured to include electronic storage medium thatelectronically stores information (e.g., non-transitory storage mediathat electronically stores information). The electronic storage 3622 maystore software algorithms, information determined by the processor 3618,information received remotely, and/or other information that enables thesystem 3600 to function properly. The electronic storage media of theelectronic storage 3622 may be provided integrally (i.e., substantiallynon-removable) with one or more components of the system 3600 and/or asremovable storage that is connectable to one or more components of thesystem 3600 via, for example, a port (e.g., a USB port, a Firewire port,etc.) or a drive (e.g., a disk drive, etc.). The electronic storage 3622may include one or more of optically readable storage media (e.g.,optical disks, etc.), magnetically readable storage media (e.g.,magnetic tape, magnetic hard drive, floppy drive, etc.), electricalcharge-based storage media (e.g., EPROM, EEPROM, RAM, etc.), solid-statestorage media (e.g., flash drive, etc.), and/or other electronicallyreadable storage media. The electronic storage 3622 may be a separatecomponent within the system 3600, or the electronic storage 3622 may beprovided integrally with one or more other components of the system 3600(e.g., the processor 3618). Although the electronic storage 3622 isshown in FIG. 36 as a single entity, this is for illustrative purposesonly. In some implementations, the electronic storage 3622 may comprisea plurality of storage units. These storage units may be physicallylocated within the same device, or the electronic storage 3622 mayrepresent storage functionality of a plurality of devices operating incoordination.

The graphical display 3624 may refer to an electronic device thatprovides visual presentation of information. The graphical display 3624may include a color display and/or a non-color display. The graphicaldisplay 3624 may be configured to visually present information. Thegraphical display 3624 may present information using/within one or moregraphical user interfaces.

The processor 3618 may be configured to provide information processingcapabilities in the system 3600. As such, the processor 3618 maycomprise one or more of a digital processor, an analog processor, adigital circuit designed to process information, a central processingunit, a graphics processing unit, a microcontroller, an analog circuitdesigned to process information, a state machine, and/or othermechanisms for electronically processing information. The processor 3618may be configured to execute one or more machine-readable instructions3602. The machine-readable instructions 3602 may include one or morecomputer program components.

It should be appreciated that although computer program components areillustrated in FIG. 36 as being co-located within a single processingunit, one or more of computer program components may be located remotelyfrom the other computer program components. While computer programcomponents are described as performing or being configured to performoperations, computer program components may comprise instructions whichmay program processor 3618 and/or system 3600 to perform the operation.

While computer program components are described herein as beingimplemented via processor 3618 through machine-readable instructions3602, this is merely for ease of reference and is not meant to belimiting. In some implementations, one or more functions of computerprogram components described herein may be implemented via hardware(e.g., dedicated chip, field-programmable gate array) rather thansoftware. One or more functions of computer program components describedherein may be software-implemented, hardware-implemented, or softwareand hardware-implemented.

The description of the functionality provided by the different computerprogram components described herein is for illustrative purposes, and isnot intended to be limiting, as any of computer program components mayprovide more or less functionality than is described. For example, oneor more of computer program components may be eliminated, and some orall of its functionality may be provided by other computer programcomponents. As another example, processor 3618 may be configured toexecute one or more additional computer program components that mayperform some or all of the functionality attributed to one or more ofcomputer program components described herein.

While particular embodiments are described above, it will be understoodit is not intended to limit the invention to these particularembodiments. On the contrary, the invention includes alternatives,modifications and equivalents that are within the spirit and scope ofthe appended claims. Numerous specific details are set forth in order toprovide a thorough understanding of the subject matter presented herein.But it will be apparent to one of ordinary skill in the art that thesubject matter may be practiced without these specific details. In otherinstances, well-known methods, procedures, components, and circuits havenot been described in detail so as not to unnecessarily obscure aspectsof the embodiments.

The terminology used in the description of the invention herein is forthe purpose of describing particular embodiments only and is notintended to be limiting of the invention. As used in the description ofthe invention and the appended claims, the singular forms “a,” “an,” and“the” are intended to include the plural forms as well, unless thecontext clearly indicates otherwise. It will also be understood that theterm “and/or” as used herein refers to and encompasses any and allpossible combinations of one or more of the associated listed items. Itwill be further understood that the terms “includes,” “including,”“comprises,” and/or “comprising,” when used in this specification,specify the presence of stated features, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, operations, elements, components, and/or groups thereof.

As used herein, the term “if” may be construed to mean “when” or “upon”or “in response to determining” or “in accordance with a determination”or “in response to detecting,” that a stated condition precedent istrue, depending on the context. Similarly, the phrase “if it isdetermined [that a stated condition precedent is true]” or “if [a statedcondition precedent is true]” or “when [a stated condition precedent istrue]” may be construed to mean “upon determining” or “in response todetermining” or “in accordance with a determination” or “upon detecting”or “in response to detecting” that the stated condition precedent istrue, depending on the context.

The use of the term “about” applies to all numeric values, whether ornot explicitly indicated. This term generally refers to a range ofnumbers that one of ordinary skill in the art would consider as areasonable amount of deviation to the recited numeric values (i.e.,having the equivalent function or result). For example, this term can beconstrued as including a deviation of ±10 percent of the given numericvalue provided such a deviation does not alter the end function orresult of the value. Therefore, a value of about 1% can be construed tobe a range from 0.9% to 1.1%. Furthermore, a range may be construed toinclude the start and the end of the range. For example, a range of 10%to 20% (i.e., range of 10%-20%) includes 10% and also includes 20%, andincludes percentages in between 10% and 20%, unless explicitly statedotherwise herein. Similarly, a range of between 10% and 20% (i.e., rangebetween 10%-20%) includes 10% and also includes 20%, and includespercentages in between 10% and 20%, unless explicitly stated otherwiseherein.

It is understood that when combinations, subsets, groups, etc. ofelements are disclosed (e.g., combinations of components in acomposition, or combinations of steps in a method), that while specificreference of each of the various individual and collective combinationsand permutations of these elements may not be explicitly disclosed, eachis specifically contemplated and described herein. By way of example, ifan item is described herein as including a component of type A, acomponent of type B, a component of type C, or any combination thereof,it is understood that this phrase describes all of the variousindividual and collective combinations and permutations of thesecomponents. For example, in some embodiments, the item described by thisphrase could include only a component of type A. In some embodiments,the item described by this phrase could include only a component of typeB. In some embodiments, the item described by this phrase could includeonly a component of type C. In some embodiments, the item described bythis phrase could include a component of type A and a component of typeB. In some embodiments, the item described by this phrase could includea component of type A and a component of type C. In some embodiments,the item described by this phrase could include a component of type Band a component of type C. In some embodiments, the item described bythis phrase could include a component of type A, a component of type B,and a component of type C. In some embodiments, the item described bythis phrase could include two or more components of type A (e.g., A1 andA2). In some embodiments, the item described by this phrase couldinclude two or more components of type B (e.g., B1 and B2). In someembodiments, the item described by this phrase could include two or morecomponents of type C (e.g., C1 and C2). In some embodiments, the itemdescribed by this phrase could include two or more of a first component(e.g., two or more components of type A (A1 and A2)), optionally one ormore of a second component (e.g., optionally one or more components oftype B), and optionally one or more of a third component (e.g.,optionally one or more components of type C). In some embodiments, theitem described by this phrase could include two or more of a firstcomponent (e.g., two or more components of type B (B1 and B2)),optionally one or more of a second component (e.g., optionally one ormore components of type A), and optionally one or more of a thirdcomponent (e.g., optionally one or more components of type C). In someembodiments, the item described by this phrase could include two or moreof a first component (e.g., two or more components of type C (C1 andC2)), optionally one or more of a second component (e.g., optionally oneor more components of type A), and optionally one or more of a thirdcomponent (e.g., optionally one or more components of type B).

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to make and use the invention. The patentable scope is defined bythe claims, and may include other examples that occur to those skilledin the art. Such other examples are intended to be within the scope ofthe claims if they have elements that do not differ from the literallanguage of the claims, or if they include equivalent elements withinsubstantial differences from the literal language of the claims.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meanings as commonly understood by one of skill in the artto which the disclosed invention belongs. All citations referred hereinare expressly incorporated by reference.

T-11543A:

This disclosure includes the following elements:

Element 1. A method of placing unique particulate tracers in asubterranean formation having a wellbore therewithin, the methodcomprising: placing unique particulate tracers in at least two stages,including a first stage and a second stage, during a hydraulicfracturing operation in a subterranean formation, wherein the uniqueparticulate tracers are pumped only in a fraction of each stage suchthat a substantial portion of the unique particulate tracers are placedin a near wellbore region of the subterranean formation proximate to thewellbore drilled into the subterranean formation, and wherein at leastone unique particulate tracer is pumped in the fraction of each stage,and wherein each unique particulate tracer corresponds to an oil phase,a water phase, or a gas phase.

Element 2. The method of element 1, further comprising determining aminimum wellbore volume between the first stage and the second stage.

Element 3. The method of element 1, further comprising determining aminimum length between the first stage and the second stage.

Element 4. The method of element 1, further comprising determining aquantity of stages without the unique particulate tracers between thefirst stage and the second stage.

Element 5. The method of element 1, further comprising determining amaximum fluid volume in a stage near the wellbore that is in contactwith unique particulate tracer once for each phase.

Element 6. The method of element 1, further comprising determining aproppant pack bulk volume once for each phase.

Element 7. The method of element 1, further comprising determining aproppant mass tagged with a unique particulate tracer once for eachphase.

Element 8. The method of element 1, further comprising determiningproppant pumped in a stage once, and utilizing the substantially sameanswer for each phase.

Element 9. The method of element 1, further comprising determining afraction of a stage in which to pump a unique particulate tracer oncefor each phase.

Element 10. The method of element 1, wherein a fraction of a stage isdetermined with an equation as follows:

${{fraction}{of}{stage}{tagged}{with}a{unique}{particulate}{tracer}} = \frac{{{Tagged}{proppant}{mass}},{lbs}}{M_{p,{stage}}{lbs}}$

wherein fraction of stage tagged with a unique particulate tracer ispercentage of a stage, tagged proppant mass is proppant mass tagged witha unique particulate tracer, and M_(p,stage) is proppant pumped in astage.

Element 11. The method of element 1, wherein a fraction of a stage inwhich to pump a unique particulate tracer comprises 0.001% to 50%.

Element 12. The method of element 1, further comprising pumping aproppant mass that is tagged with a unique particulate tracer in afraction of a stage.

Element 13. The method of element 1, further comprising determining adilution amplification factor once for each phase.

Element 14. The method of element 1, further comprising determining aunique particulate tracer mass released once for each phase.

Element 15. The method of element 1, further comprising determiningdesign particulate mass once for each phase.

Element 16. The method of element 1, further comprising determiningdesign particulate mass to tagged proppant ratio once for each phase.

Element 17. A system of placing unique particulate tracers in asubterranean formation having a wellbore therewithin, the systemcomprising: a wellbore drilled into a subterranean formation; and uniqueparticulate tracers, wherein the unique particulate tracers are placedin at least two stages, including a first stage and a second stage,during a hydraulic fracturing operation in the subterranean formation,wherein the unique particulate tracers are pumped only in a fraction ofeach stage such that a substantial portion of the unique particulatetracers are placed in a near wellbore region of the subterraneanformation proximate to the wellbore, and wherein at least one uniqueparticulate tracer is pumped in the fraction of each stage, and whereineach unique particulate tracer corresponds to an oil phase, a waterphase, or a gas phase.

Element 18. A method of determining a fraction of a stage in which toplace a unique particulate tracer, the method comprising: determining,with a physical computer processor, a fraction of a stage in which toplace a unique particulate tracer to facilitate placement of uniqueparticulate tracers in at least two stages, including a first stage anda second stage, during a hydraulic fracturing operation in asubterranean formation, wherein the unique particulate tracers arepumped only in a fraction of each stage such that a substantial portionof the unique particulate tracers are placed in a near wellbore regionof the subterranean formation proximate to the wellbore drilled into thesubterranean formation, and wherein at least one unique particulatetracer is pumped in the fraction of each stage, and wherein each uniqueparticulate tracer corresponds to an oil phase, a water phase, or a gasphase.

Element 19. The method of element 18, wherein a fraction of a stage isdetermined with an equation as follows:

${{fraction}{of}{stage}{tagged}{with}a{unique}{particulate}{tracer}} = \frac{{{Tagged}{proppant}{mass}},{lbs}}{M_{p,{stage}}{lbs}}$

wherein fraction of stage tagged with a unique particulate tracer ispercentage of a stage, tagged proppant mass is proppant mass tagged witha unique particulate tracer, and M_(p,stage) is proppant pumped in astage.

Element 20. The method of element 1, wherein a fraction of a stage inwhich to pump a unique particulate tracer comprises 0.001% to 50%.

T-11543B:

This disclosure includes the following elements:

Element 1. A method of determining a flow profile for a wellbore usingunique particulate tracers, the method comprising: obtaining producedfluid samples comprising unique particulate tracers from a wellboredrilled into a subterranean formation, wherein the unique particulatetracers are pumped in at least one stage pair during a hydraulicfracturing operation performed in the subterranean formation, andwherein the unique particulate tracers are pumped only in a fraction ofeach stage such that a substantial portion of the unique particulatetracers are placed in a near wellbore region of the subterraneanformation proximate to the wellbore, and wherein at least one uniqueparticulate tracer is pumped in the fraction of each stage, and whereineach unique particulate tracer corresponds to an oil phase, a waterphase, or a gas phase; and determining a flow profile for the wellborefor each phase using the produced fluid samples comprising the uniqueparticulate tracers by: i) obtaining a tracer concentration history foreach unique particulate tracer; ii) determining a wellbore volume forthe stage pair; and (iii) determining a flow profile for the wellborefor each phase indicative of flow contribution for each stage pair andstages within each stage pair using the wellbore volume and thecorresponding tracer concentration histories.

Element 2. The method of element 1, wherein the wellbore volume isdetermined using an equation as follows:

V _(wellbore) =L _(wellbore) ft*πr _(w) ²

wherein V_(wellbore) is wellbore volume, L_(wellbore)ft is length for aspecific stage pair, and r_(w) is a flow pipe radius.

Element 3. The method of element 1, wherein the flow contribution isdetermined using an equation as follows:

$q_{N,{{bbls}/{day}}} = \frac{V_{{wellbore},N},{({bbls})*24*60}}{{\Delta t},{minutes}}$

wherein q_(N,bbls/day) is flow contribution for a specific stage pair,V_(wellbore) is wellbore volume, Δt is arrival time difference, and N isa specific stage.

Element 4. The method of element 1, further comprising: obtaining aproduction history for the wellbore; summing all flow contributions foreach stage pair for each phase; and comparing the sums and theproduction history to constraint total flow contribution for each phase.

Element 5. The method of element 1, further comprising: smoothing atracer concentration history for a specific unique particulate tracerbefore iii) to reduce noise; and utilizing the smoothed tracerconcentration history for the specific unique particulate tracer iniii).

Element 6. The method of element 1, further comprising refining thewellbore volume in response to multiple phases in the wellbore.

Element 7. The method of element 1, further comprising: generating, on agraphical user interface, a representation of the flow profile for thewellbore for each phase indicative of the flow contribution for eachstage pair and stages within each stage pair; and displaying, via thegraphical user interface, the representation.

Element 8. A method of determining a flow profile for a wellbore usingunique particulate tracers, the method being implemented in a computersystem that includes a physical computer processor and non-transitorystorage medium, the method comprising: i) obtaining, the from anon-transitory storage medium, a tracer concentration history for eachunique particulate tracer in produced fluid samples from a wellboredrilled into a subterranean formation, wherein the unique particulatetracers are pumped in at least one stage pair during a hydraulicfracturing operation performed in the subterranean formation, andwherein the unique particulate tracers are pumped only in a fraction ofeach stage such that a substantial portion of the unique particulatetracers are placed in a near wellbore region of the subterraneanformation proximate to the wellbore, and wherein at least one uniqueparticulate tracer is pumped in the fraction of each stage, and whereineach unique particulate tracer corresponds to an oil phase, a waterphase, or a gas phase; ii) determining, with the physical computerprocessor, a wellbore volume for the stage pair; and iii) determining,with the physical computer processor, a flow profile for the wellborefor each phase indicative of flow contribution for each stage pair andstages within each stage pair using the wellbore volume and thecorresponding tracer concentration histories.

Element 9. The method of element 8, wherein the wellbore volume isdetermined using an equation as follows:

V _(wellbore) =L _(wellbore) ft*πr _(w) ²

wherein V_(wellbore) is wellbore volume, L_(wellbore)ft is length for aspecific stage pair, and r_(w) is a flow pipe radius.

Element 10. The method of element 8, wherein the flow contribution isdetermined using an equation as follows:

$q_{N,{{bbls}/{day}}} = \frac{V_{{wellbore},N},{({bbls})*24*60}}{{\Delta t},{minutes}}$

wherein q_(N,bbls/day) is flow contribution for a specific stage pair,V_(wellbore) is wellbore volume, Δt is arrival time difference, and N isa specific stage.

Element 11. The method of element 8, further comprising: obtaining aproduction history for the wellbore; summing all flow contributions foreach stage pair for each phase; and comparing the sums and theproduction history to constraint total flow contribution for each phase.

Element 12. The method of element 8, further comprising: smoothing atracer concentration history for a specific unique particulate tracerbefore iii) to reduce noise; and utilizing the smoothed tracerconcentration history for the specific unique particulate tracer iniii).

Element 13. The method of element 8, further comprising refining thewellbore volume in response to multiple phases in the wellbore.

Element 14. The method of element 8, further comprising: generating, ona graphical user interface, a representation of the flow profile for thewellbore for each phase indicative of the flow contribution for eachstage pair and stages within each stage pair; and displaying, via thegraphical user interface, the representation.

Element 15. A computer system, comprising: one or more processors;memory; and one or more programs, wherein the one or more programs arestored in the memory and configured to be executed by the one or moreprocessors, the one or more programs including instructions that whenexecuted by the one or more processors cause the system to a method ofdetermining a flow profile for a wellbore using unique particulatetracers, the method comprising: i) obtaining a tracer concentrationhistory for each unique particulate tracer in produced fluid samplesfrom a wellbore drilled into a subterranean formation, wherein theunique particulate tracers are pumped in at least one stage pair duringa hydraulic fracturing operation performed in the subterraneanformation, and wherein the unique particulate tracers are pumped only ina fraction of each stage such that a substantial portion of the uniqueparticulate tracers are placed in a near wellbore region of thesubterranean formation proximate to the wellbore, and wherein at leastone unique particulate tracer is pumped in the fraction of each stage,and wherein each unique particulate tracer corresponds to an oil phase,a water phase, or a gas phase; ii) determining a wellbore volume for thestage pair; and iii) determining a flow profile for the wellbore foreach phase indicative of flow contribution for each stage pair andstages within each stage pair using the wellbore volume and thecorresponding tracer concentration histories.

Element 16. The system of element 15, wherein the wellbore volume isdetermined using an equation as follows:

V _(wellbore) =L _(wellbore) ft*πr _(w) ²

wherein V_(wellbore) is wellbore volume, L_(wellbore)ft is length for aspecific stage pair, and r_(w) is a flow pipe radius.

Element 17. The system of element 15, wherein the flow contribution isdetermined using an equation as follows:

$q_{N,{{bbls}/{day}}} = \frac{V_{{wellbore},N},{({bbls})*24*60}}{{\Delta t},{minutes}}$

wherein q_(N,bbls/day) is flow contribution for a specific stage pair,V_(wellbore) is wellbore volume, Δt is arrival time difference, and N isa specific stage.

Element 18. The system of element 15, further comprising: obtaining aproduction history for the wellbore; summing all flow contributions foreach stage pair for each phase; and comparing the sums and theproduction history to constraint total flow contribution for each phase.

Element 19. The system of element 15, further comprising: smoothing atracer concentration history for a specific unique particulate tracerbefore iii) to reduce noise; and utilizing the smoothed tracerconcentration history for the specific unique particulate tracer iniii).

Element 20. The system of element 15, further comprising refining thewellbore volume in response to multiple phases in the wellbore.

Element 21. The system of element 15, further comprising a graphicaluser interface: generating, on the graphical user interface, arepresentation of the flow profile for the wellbore for each phaseindicative of the flow contribution for each stage pair and stageswithin each stage pair; and displaying, via the graphical userinterface, the representation.

T-11543C:

This disclosure includes the following elements:

Element 1. A method of determining a flow profile for a wellbore usingunique particulate tracers, the method comprising: obtaining producedfluid samples comprising unique particulate tracers from a wellboredrilled into a subterranean formation, wherein at least one uniqueparticulate tracer is pumped throughout each stage, each stage group, orany combination thereof during a hydraulic fracturing operationperformed in the subterranean formation, and wherein each uniqueparticulate tracer corresponds to an oil phase, a water phase, or a gasphase, and wherein the produced fluid samples comprise at least aportion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof; anddetermining a flow profile for the wellbore for each phase using theproduced fluid samples comprising the unique particulate tracers by: a)obtaining a tracer concentration history for each unique particulatetracer; b) obtaining a production history for the wellbore; c)determining a mean residence time for each unique particulate tracerusing the corresponding tracer concentration history; d) determining acontact volume proxy for each unique particulate tracer using theproduction history and the corresponding tracer concentration history;and e) determining the flow profile for the wellbore for each phaseindicative of flow contribution of each stage, each stage group, or anycombination thereof by using the corresponding mean residence times andthe corresponding contact volume proxies.

Element 2. The method of element 1, wherein the mean residence time isdetermined using an equation as follows:

$t_{res} = \frac{\int_{t = 0}^{t = \infty}{c*t*{dt}}}{\int_{t = 0}^{t = \infty}{c*{dt}}}$

wherein t_(res) is mean residence time, c is tracer concentrationhistory, t is time, and dt is integration with respect to time.

Element 3. The method of element 1, wherein the contact volume proxy isdetermined using an equation as follows:

vol_(proxy)=∫_(t=0) ^(t=∞) q*c*dt

wherein vol_(proxy) is contact volume proxy, q is production history, cis tracer concentration history, t is time, and dt is integration withrespect to time.

Element 4. The method of element 1, wherein the flow profile isdetermined using an equation as follows:

${{flow\_ contribution}_{N}(\%)} = {\frac{\frac{{vol}_{{proxy}\_ N}}{t_{{res}\_ N}}}{\sum_{i = 1}^{i = M}\frac{{vol}_{{proxy}\_ i}}{t_{{res}\_ i}}}*100}$

wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, t_(res) is mean residence time,contact_vol_(proxy) is contact volume proxy, i is a counter, M is totalnumber of stages or stage groups in which unique particulate tracerswere pumped, and N is specific stage or specific stage group for whichflow contribution is determined.

Element 5. The method of element 1, further comprising: smoothing atracer concentration history for a specific unique particulate tracerbefore c) and d) to reduce noise; and utilizing the smoothed tracerconcentration history for the specific unique particulate tracer in c)and d).

Element 6. The method of element 1, wherein the computer system furtherincludes a graphical user interface, and the method further comprises:generating, on the graphical user interface, a representation of theflow profile for the wellbore for each phase indicative of the flowcontribution of each stage, each stage group, or any combinationthereof; and displaying, via the graphical user interface, therepresentation.

Element 7. The method of element 1, before obtaining the produced fluidsamples, further comprising: shutting in the wellbore for a period oftime to cause tracer clouds to form in the subterranean formation for atleast a portion of the unique particulate tracers that were pumpedthroughout the stages, the stage groups, or any combination thereof.

Element 8. The method of element 7, after the period of time, furthercomprising flowing back the wellbore to cause produced fluid from thewellbore and the produced fluid samples are obtained from the producedfluid, and wherein the produced fluid samples comprise at least aportion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof from the tracerclouds.

Element 9. The method of element 7, further comprising analyzing theproduced fluid samples obtained from the produced fluid to generate thetracer concentration history for each unique particulate tracer.

Element 10. A method of determining a flow profile for a wellbore usingunique particulate tracers, the method being implemented in a computersystem that includes a physical computer processor and non-transitorystorage medium, the method comprising: a) obtaining, from anon-transitory storage medium, a tracer concentration history for eachunique particulate tracer in produced fluid samples from a wellboredrilled into a subterranean formation, wherein at least one uniqueparticulate tracer is pumped throughout each stage, each stage group, orany combination thereof during a hydraulic fracturing operationperformed in the subterranean formation, and wherein each uniqueparticulate tracer corresponds to an oil phase, a water phase, or a gasphase, and wherein the produced fluid samples comprise at least aportion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof; b) obtaining,from the non-transitory storage medium, a production history for thewellbore; c) determining, with a physical computer processor, a meanresidence time for each unique particulate tracer using thecorresponding tracer concentration history; d) determining, with thephysical computer processor, a contact volume proxy for each uniqueparticulate tracer using the production history and the correspondingtracer concentration history; and e) determining, with the physicalcomputer processor, a flow profile for the wellbore for each phaseindicative of flow contribution of each stage, each stage group, or anycombination thereof by using the corresponding mean residence times andthe corresponding contact volume proxies.

Element 11. The method of element 10, wherein the mean residence time isdetermined using an equation as follows:

$t_{res} = \frac{\int_{t = 0}^{t = \infty}{c*t*{dt}}}{\int_{t = 0}^{t = \infty}{c*{dt}}}$

wherein t_(res) is mean residence time, c is tracer concentrationhistory, t is time, and dt is integration with respect to time.

Element 12. The method of element 10, wherein the contact volume proxyis determined using an equation as follows:

vol_(proxy)=∫_(t=0) ^(t=∞) q*c*dt

wherein vol_(proxy) is contact volume proxy, q is production history, cis tracer concentration history, t is time, and dt is integration withrespect to time.

Element 13. The method of element 10, wherein the flow profile isdetermined using an equation as follows:

${{flow\_ contribution}_{N}(\%)} = {\frac{\frac{{vol}_{{proxy}\_ N}}{t_{{res}\_ N}}}{\sum_{i = 1}^{i = M}\frac{{vol}_{{proxy}\_ i}}{t_{{res}\_ i}}}*100}$

wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, t_(res) is mean residence time,contact_vol_(proxy) is contact volume proxy, i is a counter, M is totalnumber of stages or stage groups in which unique particulate tracerswere pumped, and N is specific stage or specific stage group for whichflow contribution is determined.

Element 14. The method of element 10, further comprising: smoothing atracer concentration history for a specific unique particulate tracerbefore c) and d) to reduce noise; and utilizing the smoothed tracerconcentration history for the specific unique particulate tracer in c)and d).

Element 15. The method of element 10, wherein the computer systemfurther includes a graphical user interface, and the method furthercomprises: generating, on the graphical user interface, a representationof the flow profile for the wellbore for each phase indicative of theflow contribution of each stage, each stage group, or any combinationthereof; and displaying, via the graphical user interface, therepresentation.

Element 16. A method of determining a flow profile for a wellbore usingunique particulate tracers, the method comprising: obtaining producedfluid samples comprising unique particulate tracers from a wellboredrilled into a subterranean formation, wherein at least one uniqueparticulate tracer is pumped throughout each stage, each stage group, orany combination thereof during a hydraulic fracturing operationperformed in the subterranean formation, and wherein each uniqueparticulate tracer corresponds to an oil phase, a water phase, or a gasphase, and wherein the produced fluid samples comprise at least aportion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof; anddetermining a flow profile for the wellbore for each phase using theproduced fluid samples comprising the unique particulate tracers by: a)obtaining a tracer concentration history for each unique particulatetracer; b) optionally obtaining a production history for the wellbore;c) determining a decline rate for each unique particulate tracer usingthe corresponding tracer concentration history; d) determining anormalization factor for each unique particulate tracer using thecorresponding tracer concentration history and optionally the productionhistory; e) determining a normalized decline rate for each uniqueparticulate tracer using the corresponding decline rate and thecorresponding normalization factor; and f) determining a flow profilefor the wellbore for each phase indicative of flow contribution of eachstage, each stage group, or any combination thereof by using thecorresponding normalized decline rates.

Element 17. The method of element 16, wherein the decline rate isdetermined using an equation as follows:

$r = \frac{dc}{dt}$

wherein r is decline rate, dC is integration with respect to tracerconcentration history, and dt is integration with respect to time.

Element 18. The method of element 16, wherein the normalization factoris represented as norm_(factor)=c_(mode)

wherein norm_factor is normalization factor and c_mode is a maximumvalue of a tracer concentration history.

Element 19. The method of element 16, wherein the normalization factoris determined using an equation as follows:

norm_(factor)=∫_(t=0) ^(t=∞) q*ρ*c*dt

wherein norm_factor is normalization factor, t is time, q is productionhistory, ρ is fluid density, c is tracer concentration history, and dtis integration with respect to time.

Element 20. The method of element 16, wherein the normalized declinerate is determined using an equation as follows:

${r\_ norm} = \frac{r}{norm\_ factor}$

wherein r_norm is normalized decline rate, r is decline rate, andnorm_factor is normalization factor.

Element 21. The method of element 16, wherein the flow profile isdetermined using an equation as follows:

${{flow\_ contribution}_{N}(\%)} = {\frac{r_{norm\_ N}}{\sum_{I = 1}^{i = M}{r_{{norm}\_}i}}*100}$

wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, r_(norm) is normalized decline rate, i is acounter, M is total number of stages or stage groups in which uniqueparticulate tracers were pumped, and N is specific stage or specificstage group for which flow contribution is determined.

Element 22. The method of element 16, further comprising: smoothing atracer concentration history for a specific unique particulate tracerbefore c) and d) to reduce noise; and utilizing the smoothed tracerconcentration history for the specific unique particulate tracer in c)and d).

Element 23. The method of element 16, wherein the computer systemfurther includes a graphical user interface, and the method furthercomprises: generating, on the graphical user interface, a representationof the flow profile for the wellbore for each phase indicative of theflow contribution of each stage, each stage group, or any combinationthereof; and displaying, via the graphical user interface, therepresentation.

Element 24. A method of determining a flow profile for a wellbore usingunique particulate tracers, the method being implemented in a computersystem that includes a physical computer processor and non-transitorystorage medium, the method comprising: a) obtaining, from anon-transitory storage medium, a tracer concentration history for eachunique particulate tracer in produced fluid samples from a wellboredrilled into a subterranean formation, wherein at least one uniqueparticulate tracer is pumped throughout each stage, each stage group, orany combination thereof during a hydraulic fracturing operationperformed in the subterranean formation, and wherein each uniqueparticulate tracer corresponds to an oil phase, a water phase, or a gasphase, and wherein the produced fluid samples comprise at least aportion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof; b) optionallyobtaining, from the non-transitory storage medium, a production historyfor the wellbore; c) determining, with a physical computer processor, adecline rate for each unique particulate tracer using the correspondingtracer concentration history; d) determining, with the physical computerprocessor, a normalization factor for each unique particulate tracerusing the corresponding tracer concentration history and optionally theproduction history; e) determining, with the physical computerprocessor, a normalized decline rate for each unique particulate tracerusing the corresponding decline rate and the corresponding normalizationfactor; and f) determining, with the physical computer processor, a flowprofile for the wellbore for each phase indicative of flow contributionof each stage, each stage group, or any combination thereof by using thecorresponding normalized decline rates.

Element 25. The method of element 24, wherein the decline rate isdetermined using an equation as follows:

$r = \frac{dc}{dt}$

wherein r is decline rate, dC is integration with respect to tracerconcentration history, and dt is integration with respect to time.

Element 26. The method of element 24, wherein the normalization factoris represented as

norm_(factor) =c _(mode)

wherein norm_factor is normalization factor and c_mode is a maximumvalue of a tracer concentration history.

Element 27. The method of element 24, wherein the normalization factoris determined using an equation as follows:

norm_(factor)=∫_(t=0) ^(t=∞) q*ρ*c*dt

wherein norm_factor is normalization factor, t is time, q is productionhistory, ρ is fluid density, c is tracer concentration history, and dtis integration with respect to time.

Element 28. The method of element 24, wherein the normalized declinerate is determined using an equation as follows:

${r\_ norm} = \frac{r}{norm\_ factor}$

wherein r_norm is normalized decline rate, r is decline rate, andnorm_factor is normalization factor.

Element 29. The method of element 24, wherein the flow profile isdetermined using an equation as follows:

${{flow\_ contribution}_{N}(\%)} = {\frac{r_{norm\_ N}}{\sum_{I = 1}^{i = M}{r_{{norm}\_}i}}*100}$

wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, r_(norm) is normalized decline rate, i is acounter, M is total number of stages or stage groups in which uniqueparticulate tracers were pumped, and N is specific stage or specificstage group for which flow contribution is determined.

Element 30. The method of element 24, further comprising: smoothing atracer concentration history for a specific unique particulate tracerbefore c) and d) to reduce noise; and utilizing the smoothed tracerconcentration history for the specific unique particulate tracer in c)and d).

Element 31. The method of element 24, wherein the computer systemfurther includes a graphical user interface, and the method furthercomprises: generating, on the graphical user interface, a representationof the flow profile for the wellbore for each phase indicative of theflow contribution of each stage, each stage group, or any combinationthereof; and displaying, via the graphical user interface, therepresentation.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit the invention to the precise forms disclosed. Many modificationsand variations are possible in view of the above teachings. Theembodiments were chosen and described in order to best explain theprinciples of the invention and its practical applications, to therebyenable others skilled in the art to best utilize the invention andvarious embodiments with various modifications as are suited to theparticular use contemplated.

What is claimed is:
 1. A method of determining a flow profile for awellbore using unique particulate tracers, the method comprising:obtaining produced fluid samples comprising unique particulate tracersfrom a wellbore drilled into a subterranean formation, wherein at leastone unique particulate tracer is pumped throughout each stage, eachstage group, or any combination thereof during a hydraulic fracturingoperation performed in the subterranean formation, and wherein eachunique particulate tracer corresponds to an oil phase, a water phase, ora gas phase, and wherein the produced fluid samples comprise at least aportion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof; anddetermining a flow profile for the wellbore for each phase using theproduced fluid samples comprising the unique particulate tracers by: a)obtaining a tracer concentration history for each unique particulatetracer; b) obtaining a production history for the wellbore; c)determining a mean residence time for each unique particulate tracerusing the corresponding tracer concentration history; d) determining acontact volume proxy for each unique particulate tracer using theproduction history and the corresponding tracer concentration history;and e) determining the flow profile for the wellbore for each phaseindicative of flow contribution of each stage, each stage group, or anycombination thereof by using the corresponding mean residence times andthe corresponding contact volume proxies.
 2. The method of claim 1,wherein the mean residence time is determined using an equation asfollows:$t_{res} = \frac{\int_{t = 0}^{t = \infty}{c*t*dt}}{\int_{t = 0}^{t = \infty}{c*dt}}$wherein t_(res) is mean residence time, c is tracer concentrationhistory, t is time, and dt is integration with respect to time.
 3. Themethod of claim 1, wherein the contact volume proxy is determined usingan equation as follows:vol_(proxy)=∫_(t=0) ^(t=∞) q*c*dt wherein vol_(proxy) is contact volumeproxy, q is production history, c is tracer concentration history, t istime, and dt is integration with respect to time.
 4. The method of claim1, wherein the flow profile is determined using an equation as follows:${{flow\_ contribution}_{N}(\%)} = {\frac{\frac{{vol}_{proxy\_ N}}{t_{res\_ N}}}{\sum_{I = 1}^{i = M}\frac{{vol}_{proxy\_ i}}{t_{res\_ i}}}*100}$wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, t_(res) is mean residence time,contact_vol_(proxy) is contact volume proxy, i is a counter, M is totalnumber of stages or stage groups in which unique particulate tracerswere pumped, and N is specific stage or specific stage group for whichflow contribution is determined.
 5. The method of claim 1, furthercomprising: smoothing a tracer concentration history for a specificunique particulate tracer before c) and d) to reduce noise; andutilizing the smoothed tracer concentration history for the specificunique particulate tracer in c) and d).
 6. The method of claim 1,wherein the computer system further includes a graphical user interface,and the method further comprises: generating, on the graphical userinterface, a representation of the flow profile for the wellbore foreach phase indicative of the flow contribution of each stage, each stagegroup, or any combination thereof; and displaying, via the graphicaluser interface, the representation.
 7. The method of claim 1, beforeobtaining the produced fluid samples, further comprising: shutting inthe wellbore for a period of time to cause tracer clouds to form in thesubterranean formation for at least a portion of the unique particulatetracers that were pumped throughout the stages, the stage groups, or anycombination thereof.
 8. The method of claim 7, after the period of time,further comprising flowing back the wellbore to cause produced fluidfrom the wellbore and the produced fluid samples are obtained from theproduced fluid, and wherein the produced fluid samples comprise at leasta portion of the unique particulate tracers that were pumped throughoutthe stages, the stage groups, or any combination thereof from the tracerclouds.
 9. The method of claim 7, further comprising analyzing theproduced fluid samples obtained from the produced fluid to generate thetracer concentration history for each unique particulate tracer.
 10. Amethod of determining a flow profile for a wellbore using uniqueparticulate tracers, the method being implemented in a computer systemthat includes a physical computer processor and non-transitory storagemedium, the method comprising: a) obtaining, from a non-transitorystorage medium, a tracer concentration history for each uniqueparticulate tracer in produced fluid samples from a wellbore drilledinto a subterranean formation, wherein at least one unique particulatetracer is pumped throughout each stage, each stage group, or anycombination thereof during a hydraulic fracturing operation performed inthe subterranean formation, and wherein each unique particulate tracercorresponds to an oil phase, a water phase, or a gas phase, and whereinthe produced fluid samples comprise at least a portion of the uniqueparticulate tracers that were pumped throughout the stages, the stagegroups, or any combination thereof; b) obtaining, from thenon-transitory storage medium, a production history for the wellbore; c)determining, with a physical computer processor, a mean residence timefor each unique particulate tracer using the corresponding tracerconcentration history; d) determining, with the physical computerprocessor, a contact volume proxy for each unique particulate tracerusing the production history and the corresponding tracer concentrationhistory; and e) determining, with the physical computer processor, aflow profile for the wellbore for each phase indicative of flowcontribution of each stage, each stage group, or any combination thereofby using the corresponding mean residence times and the correspondingcontact volume proxies.
 11. The method of claim 10, wherein the meanresidence time is determined using an equation as follows:$t_{res} = \frac{\int_{t = 0}^{t = \infty}{c*t*dt}}{\int_{t = 0}^{t = \infty}{c*dt}}$wherein t_(res) is mean residence time, c is tracer concentrationhistory, t is time, and dt is integration with respect to time.
 12. Themethod of claim 10, wherein the contact volume proxy is determined usingan equation as follows:vol_(proxy)=∫_(t=0) ^(t=∞) q*c*dt wherein vol_(proxy) is contact volumeproxy, q is production history, c is tracer concentration history, t istime, and dt is integration with respect to time.
 13. The method ofclaim 10, wherein the flow profile is determined using an equation asfollows:${{flow\_ contribution}_{N}(\%)} = {\frac{\frac{{vol}_{proxy\_ N}}{t_{res\_ N}}}{\sum_{I = 1}^{i = M}\frac{{vol}_{proxy\_ i}}{t_{res\_ i}}}*100}$wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, t_(res) is mean residence time,contact_vol_(proxy) is contact volume proxy, i is a counter, M is totalnumber of stages or stage groups in which unique particulate tracerswere pumped, and N is specific stage or specific stage group for whichflow contribution is determined.
 14. The method of claim 10, furthercomprising: smoothing a tracer concentration history for a specificunique particulate tracer before c) and d) to reduce noise; andutilizing the smoothed tracer concentration history for the specificunique particulate tracer in c) and d).
 15. The method of claim 10,wherein the computer system further includes a graphical user interface,and the method further comprises: generating, on the graphical userinterface, a representation of the flow profile for the wellbore foreach phase indicative of the flow contribution of each stage, each stagegroup, or any combination thereof; and displaying, via the graphicaluser interface, the representation.
 16. A method of determining a flowprofile for a wellbore using unique particulate tracers, the methodcomprising: obtaining produced fluid samples comprising uniqueparticulate tracers from a wellbore drilled into a subterraneanformation, wherein at least one unique particulate tracer is pumpedthroughout each stage, each stage group, or any combination thereofduring a hydraulic fracturing operation performed in the subterraneanformation, and wherein each unique particulate tracer corresponds to anoil phase, a water phase, or a gas phase, and wherein the produced fluidsamples comprise at least a portion of the unique particulate tracersthat were pumped throughout the stages, the stage groups, or anycombination thereof; and determining a flow profile for the wellbore foreach phase using the produced fluid samples comprising the uniqueparticulate tracers by: a) obtaining a tracer concentration history foreach unique particulate tracer; b) optionally obtaining a productionhistory for the wellbore; c) determining a decline rate for each uniqueparticulate tracer using the corresponding tracer concentration history;d) determining a normalization factor for each unique particulate tracerusing the corresponding tracer concentration history and optionally theproduction history; e) determining a normalized decline rate for eachunique particulate tracer using the corresponding decline rate and thecorresponding normalization factor; and f) determining a flow profilefor the wellbore for each phase indicative of flow contribution of eachstage, each stage group, or any combination thereof by using thecorresponding normalized decline rates.
 17. The method of claim 16,wherein the decline rate is determined using an equation as follows:$r = \frac{dc}{dt}$ wherein r is decline rate, dC is integration withrespect to tracer concentration history, and dt is integration withrespect to time.
 18. The method of claim 16, wherein the normalizationfactor is represented asnorm_(factor) =c _(mode) wherein norm_factor is normalization factor andc_mode is a maximum value of a tracer concentration history.
 19. Themethod of claim 16, wherein the normalization factor is determined usingan equation as follows:norm_(factor)=∫_(t=0) ^(t=∞) q*ρ*c*dt wherein norm_factor isnormalization factor, t is time, q is production history, ρ is fluiddensity, c is tracer concentration history, and dt is integration withrespect to time.
 20. The method of claim 16, wherein the normalizeddecline rate is determined using an equation as follows:${r\_ norm} = \frac{r}{norm\_ factor}$ wherein r_norm is normalizeddecline rate, r is decline rate, and norm_factor is normalizationfactor.
 21. The method of claim 16, wherein the flow profile isdetermined using an equation as follows:${{flow\_ contribution}_{N}(\%)} = {\frac{r_{norm\_ N}}{\sum_{I = 1}^{i = M}{r_{{norm}\_}i}}*100}$wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, r_(norm) is normalized decline rate, i is acounter, M is total number of stages or stage groups in which uniqueparticulate tracers were pumped, and N is specific stage or specificstage group for which flow contribution is determined.
 22. The method ofclaim 16, further comprising: smoothing a tracer concentration historyfor a specific unique particulate tracer before c) and d) to reducenoise; and utilizing the smoothed tracer concentration history for thespecific unique particulate tracer in c) and d).
 23. The method of claim16, wherein the computer system further includes a graphical userinterface, and the method further comprises: generating, on thegraphical user interface, a representation of the flow profile for thewellbore for each phase indicative of the flow contribution of eachstage, each stage group, or any combination thereof; and displaying, viathe graphical user interface, the representation.
 24. A method ofdetermining a flow profile for a wellbore using unique particulatetracers, the method being implemented in a computer system that includesa physical computer processor and non-transitory storage medium themethod comprising: a) obtaining, from a non-transitory storage medium, atracer concentration history for each unique particulate tracer inproduced fluid samples from a wellbore drilled into a subterraneanformation, wherein at least one unique particulate tracer is pumpedthroughout each stage, each stage group, or any combination thereofduring a hydraulic fracturing operation performed in the subterraneanformation, and wherein each unique particulate tracer corresponds to anoil phase, a water phase, or a gas phase, and wherein the produced fluidsamples comprise at least a portion of the unique particulate tracersthat were pumped throughout the stages, the stage groups, or anycombination thereof; b) optionally obtaining, from the non-transitorystorage medium, a production history for the wellbore; c) determining,with a physical computer processor, a decline rate for each uniqueparticulate tracer using the corresponding tracer concentration history;d) determining, with the physical computer processor, a normalizationfactor for each unique particulate tracer using the corresponding tracerconcentration history and optionally the production history; e)determining, with the physical computer processor, a normalized declinerate for each unique particulate tracer using the corresponding declinerate and the corresponding normalization factor; and f) determining,with the physical computer processor, a flow profile for the wellborefor each phase indicative of flow contribution of each stage, each stagegroup, or any combination thereof by using the corresponding normalizeddecline rates.
 25. The method of claim 24, wherein the decline rate isdetermined using an equation as follows: $r = \frac{dc}{dt}$ wherein ris decline rate, dC is integration with respect to tracer concentrationhistory, and dt is integration with respect to time.
 26. The method ofclaim 24, wherein the normalization factor is represented asnorm_(factor) =c _(mode) wherein norm_factor is normalization factor andc_mode is a maximum value of a tracer concentration history.
 27. Themethod of claim 24, wherein the normalization factor is determined usingan equation as follows:norm_(factor)=∫_(t=0) ^(t=∞) q*ρ*c*dt wherein norm_factor isnormalization factor, t is time, q is production history, ρ is fluiddensity, c is tracer concentration history, and dt is integration withrespect to time.
 28. The method of claim 24, wherein the normalizeddecline rate is determined using an equation as follows:${r\_ norm} = \frac{r}{norm\_ factor}$ wherein r_norm is normalizeddecline rate, r is decline rate, and norm_factor is normalizationfactor.
 29. The method of claim 24, wherein the flow profile isdetermined using an equation as follows:${{flow\_ contribution}_{N}(\%)} = {\frac{r_{norm\_ N}}{\sum_{I = 1}^{i = M}{r_{{norm}\_}i}}*100}$wherein flow_contribution_(N) is flow contribution for a specific stageor specific stage group, r_(norm) is normalized decline rate, i is acounter, M is total number of stages or stage groups in which uniqueparticulate tracers were pumped, and N is specific stage or specificstage group for which flow contribution is determined.
 30. The method ofclaim 24, further comprising: smoothing a tracer concentration historyfor a specific unique particulate tracer before c) and d) to reducenoise; and utilizing the smoothed tracer concentration history for thespecific unique particulate tracer in c) and d).
 31. The method of claim24, wherein the computer system further includes a graphical userinterface, and the method further comprises: generating, on thegraphical user interface, a representation of the flow profile for thewellbore for each phase indicative of the flow contribution of eachstage, each stage group, or any combination thereof; and displaying, viathe graphical user interface, the representation.